In mathematics, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundleP over a smooth manifoldM is a particular type of connection which is compatible with the action of the group G.
Let π:P→M be a smooth principal G-bundle over a smooth manifoldM. Then a principal G-connection on P is a differential 1-form on Pwith values in the Lie algebra of G which is G-equivariant and reproduces the Lie algebra generators of the fundamental vector fields on P.
An affine bundle is a fiber bundle with a general affinestructure group of affine transformations of its typical fiber of dimension . Therefore, an affine connection is associated to a principal connection. It always exists.
For any affine connection , the corresponding linear derivative of an affine morphism defines a
unique linear connection on a vector bundle . With respect to linear bundle
coordinates on , this connection reads
Since every vector bundle is an affine bundle, any linear connection on
a vector bundle also is an affine connection.
If is a vector bundle, both an affine connection
and an associated linear connection are
connections on the same vector bundle , and their
difference is a basic soldering form on . Thus, every affine
connection on a vector bundle is a sum of a linear
connection and a basic soldering form on .
"Connection" is a song released by the Britpop group Elastica. It was originally released in 1994 as a single and the album version was not released until 1995 on their self-titled debut.
The song was the subject of controversy, due to its overt similarity to another band's work. The intro synthesizer part (later repeated as a guitar figure) is lifted from the guitar riff in Wire's "Three Girl Rhumba" and transposed down a semitone. A judgment resulted in an out-of-court settlement and the credits were rewritten.
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. Physical space is often conceived in three lineardimensions, although modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework.
In 2008 the logo was changed along with the programming and idents.
Programming
NBA on TNT games (narrated and commented by Leo Montero and Daniel Jacubovich in Spanish, Marcos César and Fabio Malavazzi in Portuguese; former basketball star Maria Paula Silva also comments during the playoffs and All-Star Game)
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Affine connection
In the branch of mathematics called differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, and so permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space.The notion of an affine connection has its roots in 19th-century geometry and tensor calculus, but was not fully developed until the early 1920s, by Élie Cartan (as part of his general theory of connections) and Hermann Weyl (who used the notion as a part of his foundations for general relativity).
=======Image-Copyright-Info========
License: Creative C...
published: 22 Jan 2016
AFFINE CONNECTION
WE NEED TO FIND CORRECTION TERM WHEN WE SWITCH FROM ONE COORDINATE SYSTEM TO ANOTHER IN CURVED SPACE,THIS TERM IS CALLED AFFINE CONNECTION.
This video looks at the concept of an affine connection and its role in connecting nearby tangent spaces on manifolds which, in turn, enables the differentiation of vector fields on these manifolds. It shows how the connection is a geometric object and then looks at what form the symbol used to label this object takes.
published: 07 Dec 2019
Affine connections on linear manifolds
published: 15 Feb 2021
General Relativity - U02 Lecture Affine Connections
Affine Connections
. (Covariant) Derivative Operator
. Relation between different derivative operators
. Torsion free condition
. Transformation of Christoffel symbols
. Metric compatibility
. Divergence of vector field
. Directional covariant derivative
. Parallel transport
. Covariant derivative definition from parallel transport
------------------------------------------------------------
Supplementary material for the undergraduate course “General Relativity and Cosmology” offered at the Physics Department of the School of Applied Mathematical and Physical Sciences of the National Technical University of Athens (NTUA).
Related page: http://physics.ntua.gr/konstant/GR/
Instructor:
Konstantinos N. Anagnostopoulos (spring 2023), Associate Professor of Physics, NTUA
http://physics...
Defining some terms:
Levi-Civita Connection – this form of the Christoffel symbol comes from a form of the covariant derivative known as the Levi-Civita Connection
- Torsion free, metric compatible covariant derivative
Leibniz Rule – covariant derivative of a scaled vector – covariant derivative of component (scalar) and basis vector (vector)
Connection (affine connection) – the covariant derivative is sometimes called the Connection because it tells you how to connect different parts of the manifold
Torsion Free – the indices can be switched around
Metric Compatibility – the dot product of two vectors at one part of the manifold (in one tangent space) is preserved when parallel transported to another part of the manifold (another tangent space)
Lecture Notes:
https://authortomharp...
published: 06 Dec 2021
linear connection or affine connection
published: 10 Apr 2023
Affine connections & covariant derivative
Di video ini dijelaskan konsep affine connections dan turunan kovarian
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Affine connection
In the branch...
If you find our videos helpful you can support us by buying something from amazon.
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Affine connection
In the branch of mathematics called differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, and so permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space.The notion of an affine connection has its roots in 19th-century geometry and tensor calculus, but was not fully developed until the early 1920s, by Élie Cartan (as part of his general theory of connections) and Hermann Weyl (who used the notion as a part of his foundations for general relativity).
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License: Creative Commons Attribution-Share Alike 3.0 (CC-BY-SA-3.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/3.0/
Author: Silly rabbit
Link: //en.wikipedia.org/wiki/User:Silly_rabbit
Author-Info: Silly rabbit at English Wikipedia
Image Source: https://en.wikipedia.org/wiki/File:Parallel_transport_sphere.svg
=======Image-Copyright-Info========
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=i3zTrLsNT5E
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Affine connection
In the branch of mathematics called differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, and so permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space.The notion of an affine connection has its roots in 19th-century geometry and tensor calculus, but was not fully developed until the early 1920s, by Élie Cartan (as part of his general theory of connections) and Hermann Weyl (who used the notion as a part of his foundations for general relativity).
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 3.0 (CC-BY-SA-3.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/3.0/
Author: Silly rabbit
Link: //en.wikipedia.org/wiki/User:Silly_rabbit
Author-Info: Silly rabbit at English Wikipedia
Image Source: https://en.wikipedia.org/wiki/File:Parallel_transport_sphere.svg
=======Image-Copyright-Info========
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=i3zTrLsNT5E
This video looks at the concept of an affine connection and its role in connecting nearby tangent spaces on manifolds which, in turn, enables the differentiatio...
This video looks at the concept of an affine connection and its role in connecting nearby tangent spaces on manifolds which, in turn, enables the differentiation of vector fields on these manifolds. It shows how the connection is a geometric object and then looks at what form the symbol used to label this object takes.
This video looks at the concept of an affine connection and its role in connecting nearby tangent spaces on manifolds which, in turn, enables the differentiation of vector fields on these manifolds. It shows how the connection is a geometric object and then looks at what form the symbol used to label this object takes.
Affine Connections
. (Covariant) Derivative Operator
. Relation between different derivative operators
. Torsion free condition
. Transformation of Christoffel...
Affine Connections
. (Covariant) Derivative Operator
. Relation between different derivative operators
. Torsion free condition
. Transformation of Christoffel symbols
. Metric compatibility
. Divergence of vector field
. Directional covariant derivative
. Parallel transport
. Covariant derivative definition from parallel transport
------------------------------------------------------------
Supplementary material for the undergraduate course “General Relativity and Cosmology” offered at the Physics Department of the School of Applied Mathematical and Physical Sciences of the National Technical University of Athens (NTUA).
Related page: http://physics.ntua.gr/konstant/GR/
Instructor:
Konstantinos N. Anagnostopoulos (spring 2023), Associate Professor of Physics, NTUA
http://physics.ntua.gr/konstant
Affine Connections
. (Covariant) Derivative Operator
. Relation between different derivative operators
. Torsion free condition
. Transformation of Christoffel symbols
. Metric compatibility
. Divergence of vector field
. Directional covariant derivative
. Parallel transport
. Covariant derivative definition from parallel transport
------------------------------------------------------------
Supplementary material for the undergraduate course “General Relativity and Cosmology” offered at the Physics Department of the School of Applied Mathematical and Physical Sciences of the National Technical University of Athens (NTUA).
Related page: http://physics.ntua.gr/konstant/GR/
Instructor:
Konstantinos N. Anagnostopoulos (spring 2023), Associate Professor of Physics, NTUA
http://physics.ntua.gr/konstant
Defining some terms:
Levi-Civita Connection – this form of the Christoffel symbol comes from a form of the covariant derivative known as the Levi-Civita Connec...
Defining some terms:
Levi-Civita Connection – this form of the Christoffel symbol comes from a form of the covariant derivative known as the Levi-Civita Connection
- Torsion free, metric compatible covariant derivative
Leibniz Rule – covariant derivative of a scaled vector – covariant derivative of component (scalar) and basis vector (vector)
Connection (affine connection) – the covariant derivative is sometimes called the Connection because it tells you how to connect different parts of the manifold
Torsion Free – the indices can be switched around
Metric Compatibility – the dot product of two vectors at one part of the manifold (in one tangent space) is preserved when parallel transported to another part of the manifold (another tangent space)
Lecture Notes:
https://authortomharper.com/wp-content/uploads/2021/12/Tensors-Lecture-6-Notes-4.pdf
Other places you can find content from me:
Patreon - authortomharper
https://www.patreon.com/authortomharper
Blog - The Cynical Philosopher
https://authortomharper.com/
Twitter - @AuthorTomHarper
https://twitter.com/AuthorTomHarper
Amazon - Author Profile
https://www.amazon.com/Thomas-Harper/e/B00P73KHWG/ref=dp_byline_cont_book_1
My science fiction series available on Amazon
Incarnate: Existence
Incarnate: Essence
Incarnate: Schism
Other Resources
Profound Physics: https://profoundphysics.com/the-ricci-tensor/
Youtube Playlists on Tensors
eigenchris
Tensors for Beginners: https://www.youtube.com/playlist?list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG
Tensor Calculus: https://www.youtube.com/playlist?list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx
Relativity: https://www.youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQa
Andrew Dotson
New to Tensors? https://www.youtube.com/playlist?list=PLSuQRd4LfSUTmb_7IK7kAzxJtU2tpmEd3
XylyXylyX
What is a Tensor? https://www.youtube.com/playlist?list=PLRlVmXqzHjUQARA37r4Qw3SHPqVXgqO6c
What is General Relativity? https://www.youtube.com/playlist?list=PLRlVmXqzHjURQIIebhT7UNTwGQHUEPlsb
Books
*A Student’s Guide to Vectors and Tensors* by Daniel A. Fleisch
https://www.amazon.com/Students-Guide-Vectors-Tensors-Guides/dp/0521171903/
*Spacetime and Geometry: An Introduction to General Relativity* by Sean M. Carroll
https://www.amazon.com/Spacetime-Geometry-Introduction-General-Relativity/dp/1108488390/
Defining some terms:
Levi-Civita Connection – this form of the Christoffel symbol comes from a form of the covariant derivative known as the Levi-Civita Connection
- Torsion free, metric compatible covariant derivative
Leibniz Rule – covariant derivative of a scaled vector – covariant derivative of component (scalar) and basis vector (vector)
Connection (affine connection) – the covariant derivative is sometimes called the Connection because it tells you how to connect different parts of the manifold
Torsion Free – the indices can be switched around
Metric Compatibility – the dot product of two vectors at one part of the manifold (in one tangent space) is preserved when parallel transported to another part of the manifold (another tangent space)
Lecture Notes:
https://authortomharper.com/wp-content/uploads/2021/12/Tensors-Lecture-6-Notes-4.pdf
Other places you can find content from me:
Patreon - authortomharper
https://www.patreon.com/authortomharper
Blog - The Cynical Philosopher
https://authortomharper.com/
Twitter - @AuthorTomHarper
https://twitter.com/AuthorTomHarper
Amazon - Author Profile
https://www.amazon.com/Thomas-Harper/e/B00P73KHWG/ref=dp_byline_cont_book_1
My science fiction series available on Amazon
Incarnate: Existence
Incarnate: Essence
Incarnate: Schism
Other Resources
Profound Physics: https://profoundphysics.com/the-ricci-tensor/
Youtube Playlists on Tensors
eigenchris
Tensors for Beginners: https://www.youtube.com/playlist?list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG
Tensor Calculus: https://www.youtube.com/playlist?list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx
Relativity: https://www.youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQa
Andrew Dotson
New to Tensors? https://www.youtube.com/playlist?list=PLSuQRd4LfSUTmb_7IK7kAzxJtU2tpmEd3
XylyXylyX
What is a Tensor? https://www.youtube.com/playlist?list=PLRlVmXqzHjUQARA37r4Qw3SHPqVXgqO6c
What is General Relativity? https://www.youtube.com/playlist?list=PLRlVmXqzHjURQIIebhT7UNTwGQHUEPlsb
Books
*A Student’s Guide to Vectors and Tensors* by Daniel A. Fleisch
https://www.amazon.com/Students-Guide-Vectors-Tensors-Guides/dp/0521171903/
*Spacetime and Geometry: An Introduction to General Relativity* by Sean M. Carroll
https://www.amazon.com/Spacetime-Geometry-Introduction-General-Relativity/dp/1108488390/
If you find our videos helpful you can support us by buying something from amazon.
https://www.amazon.com/?tag=wiki-audio-20
Affine connection
In the branch of mathematics called differential geometry, an affine connection is a geometric object on a smooth manifold which connects nearby tangent spaces, and so permits tangent vector fields to be differentiated as if they were functions on the manifold with values in a fixed vector space.The notion of an affine connection has its roots in 19th-century geometry and tensor calculus, but was not fully developed until the early 1920s, by Élie Cartan (as part of his general theory of connections) and Hermann Weyl (who used the notion as a part of his foundations for general relativity).
=======Image-Copyright-Info========
License: Creative Commons Attribution-Share Alike 3.0 (CC-BY-SA-3.0)
LicenseLink: http://creativecommons.org/licenses/by-sa/3.0/
Author: Silly rabbit
Link: //en.wikipedia.org/wiki/User:Silly_rabbit
Author-Info: Silly rabbit at English Wikipedia
Image Source: https://en.wikipedia.org/wiki/File:Parallel_transport_sphere.svg
=======Image-Copyright-Info========
-Video is targeted to blind users
Attribution:
Article text available under CC-BY-SA
image source in video
https://www.youtube.com/watch?v=i3zTrLsNT5E
This video looks at the concept of an affine connection and its role in connecting nearby tangent spaces on manifolds which, in turn, enables the differentiation of vector fields on these manifolds. It shows how the connection is a geometric object and then looks at what form the symbol used to label this object takes.
Affine Connections
. (Covariant) Derivative Operator
. Relation between different derivative operators
. Torsion free condition
. Transformation of Christoffel symbols
. Metric compatibility
. Divergence of vector field
. Directional covariant derivative
. Parallel transport
. Covariant derivative definition from parallel transport
------------------------------------------------------------
Supplementary material for the undergraduate course “General Relativity and Cosmology” offered at the Physics Department of the School of Applied Mathematical and Physical Sciences of the National Technical University of Athens (NTUA).
Related page: http://physics.ntua.gr/konstant/GR/
Instructor:
Konstantinos N. Anagnostopoulos (spring 2023), Associate Professor of Physics, NTUA
http://physics.ntua.gr/konstant
Defining some terms:
Levi-Civita Connection – this form of the Christoffel symbol comes from a form of the covariant derivative known as the Levi-Civita Connection
- Torsion free, metric compatible covariant derivative
Leibniz Rule – covariant derivative of a scaled vector – covariant derivative of component (scalar) and basis vector (vector)
Connection (affine connection) – the covariant derivative is sometimes called the Connection because it tells you how to connect different parts of the manifold
Torsion Free – the indices can be switched around
Metric Compatibility – the dot product of two vectors at one part of the manifold (in one tangent space) is preserved when parallel transported to another part of the manifold (another tangent space)
Lecture Notes:
https://authortomharper.com/wp-content/uploads/2021/12/Tensors-Lecture-6-Notes-4.pdf
Other places you can find content from me:
Patreon - authortomharper
https://www.patreon.com/authortomharper
Blog - The Cynical Philosopher
https://authortomharper.com/
Twitter - @AuthorTomHarper
https://twitter.com/AuthorTomHarper
Amazon - Author Profile
https://www.amazon.com/Thomas-Harper/e/B00P73KHWG/ref=dp_byline_cont_book_1
My science fiction series available on Amazon
Incarnate: Existence
Incarnate: Essence
Incarnate: Schism
Other Resources
Profound Physics: https://profoundphysics.com/the-ricci-tensor/
Youtube Playlists on Tensors
eigenchris
Tensors for Beginners: https://www.youtube.com/playlist?list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG
Tensor Calculus: https://www.youtube.com/playlist?list=PLJHszsWbB6hpk5h8lSfBkVrpjsqvUGTCx
Relativity: https://www.youtube.com/playlist?list=PLJHszsWbB6hqlw73QjgZcFh4DrkQLSCQa
Andrew Dotson
New to Tensors? https://www.youtube.com/playlist?list=PLSuQRd4LfSUTmb_7IK7kAzxJtU2tpmEd3
XylyXylyX
What is a Tensor? https://www.youtube.com/playlist?list=PLRlVmXqzHjUQARA37r4Qw3SHPqVXgqO6c
What is General Relativity? https://www.youtube.com/playlist?list=PLRlVmXqzHjURQIIebhT7UNTwGQHUEPlsb
Books
*A Student’s Guide to Vectors and Tensors* by Daniel A. Fleisch
https://www.amazon.com/Students-Guide-Vectors-Tensors-Guides/dp/0521171903/
*Spacetime and Geometry: An Introduction to General Relativity* by Sean M. Carroll
https://www.amazon.com/Spacetime-Geometry-Introduction-General-Relativity/dp/1108488390/
In mathematics, a connection is a device that defines a notion of parallel transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundleP over a smooth manifoldM is a particular type of connection which is compatible with the action of the group G.
Let π:P→M be a smooth principal G-bundle over a smooth manifoldM. Then a principal G-connection on P is a differential 1-form on Pwith values in the Lie algebra of G which is G-equivariant and reproduces the Lie algebra generators of the fundamental vector fields on P.
Feat. KJ and Lil Won Bitch we outta space Smokin on kush don't ask me why smell the loud when you passin by come sit on mars with this astrounaut Bitch we outta space Smokin floatin loaded speakin in slow motion I can barely even focus Bitch we outta space [KJ] I'm on a kush cloud pow Nigga smokin dat loud wow Hoes flock to my squad because they see the drugs we around that's how we get down astronaut clique gotta flawless style we do it grande fam cigarillos get broke down light the kush baseball da blunt homerun smoker sammy sosa I got that kush I thought you knew cuz One day we on clouds me won swat das how we get down posted loaded floatin an these chicks started smelling that loud approaching why woos like can we join I'm like you gotta set of titties hit tht blunt won stupid faded swat stupid faded these chicks was dtf so you kno how we played it the slips one nation an I'm like mannnn We da astrounaut clique An we bout to take off nigga Make yo chick my astrounaut bitch Always on mary jane nigga We da astronaut clique so respect my mind nigga the slip takin over shit an I'm like mannnnn Bitch we outta space Smokin on kush don't ask me why smell the loud when you passin by come sit on mars with this astronaut Bitch we outta space Smokin floatin loaded speakin in slow motion I can barely even focus Bitch we outta space [Won] Whoo I'm high mannn I'm loaded I'm floating steady smoking on potent potion not fokus on where a nigga going So I jux sit in a daze headed ta space don't judge my ways I'm On dat plane witcho main nd she giving me face U walk by nd u smell da kush nd look & stare n amazement Kuz it's loud as hell nd u kant tell either if I'm black or I'm Asian Kuz.My eyes low like I'm on hydro But I'm not I'm jux on kloud 9 Where ever I go u know I blow on kouple grams up to a ounce I'm gon ima astronaut sooo don't ask me why R u tryna choke on this purple loud if not u need to move the fuck around Big chief on dis dodo slo tho kuz ion really solo ya bozo Klown lookin ass homo pop wit ya fofo bang bang like my name robo So split it fill it twist it lick it then light that hoe up Puff puff pass chug that gas that feeling is real huh If I'm lifted I ain't trippn bcuz my life is too geechie Bitch I'm outta space wit my brotha k nd my patna swateezy Yea won Bitch we outta space Smokin on kush don't ask me why smell the loud when you passin by come sit on mars with this astronaut Bitch we outta space Smokin floatin loaded speakin in slow motion I can barely even focus Bitch we outta space [Swat] I'm speakin in slow motion Smoking on that potent Weed loud it's a commotion I'm feelin myself wheres the lotion We got the plan in motion Troy and clay they coachin Burning bread we toastin Eyes red and they loccing There's no one in the city even close to fuckin with me Yeah I'm fuckin dope like bobby and whitney Puff puff pass and we smokin like a chimney Kj won and a couple others with me You must heard I'm hot dog gettin relish so you better katchup Il take ya bitch and pass the blunt Like a stuffy nose she backin up Man these hoes be actin up But I got them in check casanova shit She get hard knocked that hova shit We in the stars supernova shit Kj I swear this the shit that we been made for Talk is cheap so imma show them what they paid for I spread her like a butter knife while you tryna spoon But I'm forkin, twistin like contortion She hot, scorching tongue all on my forskin Fuck her then I'm out this bitch, like an abortion