Non-trivial explicit example of a flat connection
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We all know that the exterior derivative on the trivial bundle forms an example of a flat connection. Can anyone provide an explicit example of a flat connection that is not just the exterior derivative?
I am well aware that this is very likely a trivial question.
riemannian-geometry vector-bundles connections
asked Dec 9 '18 at 3:03
AmorFatiAmorFati
406529
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add a comment |
$begingroup$
We all know that the exterior derivative on the trivial bundle forms an example of a flat connection. Can anyone provide an explicit example of a flat connection that is not just the exterior derivative?
I am well aware that this is very likely a trivial question.
riemannian-geometry vector-bundles connections
asked Dec 9 '18 at 3:03
AmorFatiAmorFati
406529
$endgroup$
add a comment |
$begingroup$
We all know that the exterior derivative on the trivial bundle forms an example of a flat connection. Can anyone provide an explicit example of a flat connection that is not just the exterior derivative?
I am well aware that this is very likely a trivial question.
riemannian-geometry vector-bundles connections
asked Dec 9 '18 at 3:03
AmorFatiAmorFati
406529
$endgroup$
We all know that the exterior derivative on the trivial bundle forms an example of a flat connection. Can anyone provide an explicit example of a flat connection that is not just the exterior derivative?
I am well aware that this is very likely a trivial question.
riemannian-geometry vector-bundles connections
riemannian-geometry vector-bundles connections
asked Dec 9 '18 at 3:03
AmorFatiAmorFati
406529
asked Dec 9 '18 at 3:03
AmorFatiAmorFati
406529
asked Dec 9 '18 at 3:03
AmorFatiAmorFati
406529
asked Dec 9 '18 at 3:03
AmorFatiAmorFati
406529
asked Dec 9 '18 at 3:03
AmorFatiAmorFati
406529
406529
add a comment |
add a comment |
1 Answer
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You may want a flat torus; or even more simply a cylinder.
answered Dec 9 '18 at 3:29
Chris CusterChris Custer
12.1k3825
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
You may want a flat torus; or even more simply a cylinder.
answered Dec 9 '18 at 3:29
Chris CusterChris Custer
12.1k3825
$endgroup$
add a comment |
$begingroup$
You may want a flat torus; or even more simply a cylinder.
answered Dec 9 '18 at 3:29
Chris CusterChris Custer
12.1k3825
$endgroup$
add a comment |
$begingroup$
You may want a flat torus; or even more simply a cylinder.
answered Dec 9 '18 at 3:29
Chris CusterChris Custer
12.1k3825
$endgroup$
You may want a flat torus; or even more simply a cylinder.
answered Dec 9 '18 at 3:29
Chris CusterChris Custer
12.1k3825
answered Dec 9 '18 at 3:29
Chris CusterChris Custer
12.1k3825
answered Dec 9 '18 at 3:29
Chris CusterChris Custer
12.1k3825
answered Dec 9 '18 at 3:29
Chris CusterChris Custer
12.1k3825
12.1k3825
add a comment |
add a comment |
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