List questions from connections

Published on 12 Apr 2021 - 0:49

672

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Levi-Civita Connection in $\mathbb{R}^n$

Published on 13 Apr 2021 - 13:39

93

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Is there a natural extension of Levi-Civita connection to include torsion?

Published on 15 Apr 2021 - 22:42

67

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Connections on vector bundles: how they allow us to differentiate sections and to identify fibers?

Published on 23 Apr 2021 - 20:22

182

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Why is the covariant derivative defined as $\nabla_{X}Y=P((X\otimes I)Y)$, projection onto the space of all vector fields, in this wikipedia article?

Published on 25 Apr 2021 - 22:21

94

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Questions about Connections on normal bundles & infinitesimal action of a vector field

Published on 27 Apr 2021 - 0:44

206

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Cylinder Parallel Transport

Published on 27 Apr 2021 - 20:13

179

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On the proof about the dimension of the conformal group of a manifold

Published on 26 Mar 2026 - 13:52

143

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Connection on a bundle

Published on 04 May 2021 - 19:53

307

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What kind of connection is the directional derivative?

Published on 05 May 2021 - 13:11

351

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Local coordinates of one form on a principal bundle

Published on 28 Mar 2026 - 2:22

65

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Calculating the variation of a scalar field along the two parameter variation $\alpha(t; r, s) = \exp_{x(t)}(rV(t) + sW(t))$

Published on 24 Feb 2026 - 3:52

90

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Why does $\nabla_{X}Y$ depend only on $X_{p}$? Lee's book on Riemannian geometry

Published on 17 May 2021 - 12:23

158

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Reference request on Ehresmann connections

Published on 19 May 2021 - 1:44

45

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Connection on isomorphic principal bundle

Published on 28 Mar 2026 - 2:21

List Question

Question about covariant derivative on a vector bundle

Levi-Civita Connection in $\mathbb{R}^n$

Is there a natural extension of Levi-Civita connection to include torsion?

Connections on vector bundles: how they allow us to differentiate sections and to identify fibers?

Why is the covariant derivative defined as $\nabla_{X}Y=P((X\otimes I)Y)$, projection onto the space of all vector fields, in this wikipedia article?

Questions about Connections on normal bundles & infinitesimal action of a vector field

Cylinder Parallel Transport

On the proof about the dimension of the conformal group of a manifold

Connection on a bundle

What kind of connection is the directional derivative?

Local coordinates of one form on a principal bundle

Calculating the variation of a scalar field along the two parameter variation $\alpha(t; r, s) = \exp_{x(t)}(rV(t) + sW(t))$

Why does $\nabla_{X}Y$ depend only on $X_{p}$? Lee's book on Riemannian geometry

Reference request on Ehresmann connections

Connection on isomorphic principal bundle

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