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Results tagged with connections
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user 24078
Ehresmann connections; covariant derivatives; connections on vector bundles, principal bundles, ∞-bundles, submersions, bundle gerbes; holonomy and higher holonomy; parallel transport; torsion; curvature. See also the tags [principal-bundles], [vector-bundles], [gerbes], [curvature], [geodesics], [characteristic-classes], [torsion].
5
votes
2
answers
649
views
Most natural connection on Lie group: comparison of different pictures
Let $G$ be a Lie group (not necessarily compact). One can equip $G$ with the left invariant metric (or
right invariant but in general there is no biinvariant metric in the noncompact case). Once the …
- 9,340
9
votes
1
answer
677
views
Generalized Dirac operators
So far I met three definitions of the so called generalized Dirac operator(or Dirac type operators. Everything takes place over Riemannian manifols $M$ and we have smooth hermitian vector bundle $S \t …
- 9,340
23
votes
3
answers
5k
views
Manifolds admitting flat connections
Question 2 Is it possible to find a manifold $M$ with the following property: for each Riemannian metric tensor $g$ the corresponding Levi Civita connection is not flat but still there are flat torsion-free connections … Question 3 Is it possible to find a manifold $M$ with the following property: each torsion free connection cannot be flat but still there are some flat connections on $M$? …
- 9,340