Question

Affine connections: how to show that $\sum_{ij} x_i X_i(y_j)X_j = \sum_k X(y_k) X_k$?

score 169 · Answer 1 · 2017-01-21 04:19:18

169

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Affine connections: how to show that $\sum_{ij} x_i X_i(y_j)X_j = \sum_k X(y_k) X_k$?

Published on 21 Jan 2017 - 4:19

score 436 · Answer 2 · 2017-01-22 04:42:25

436

Views

For a vector bundle $\xi:E\to M$, why is Trace a parallel section of the bundle $End(\xi)^*$?

Published on 22 Jan 2017 - 4:42

score 283 · Answer 3 · 2026-03-25 22:04:02

283

Views

Do the Chern classes of a principal bundle depend on an embedding $G\hookrightarrow U(n)$?

Published on 25 Mar 2026 - 22:04

score 105 · Answer 4 · 2017-01-24 22:09:51

105

Views

Book/Slides/Videos about points-topology-manifold-charts-riemannian manifolds etc

Published on 24 Jan 2017 - 22:09

score 1.6k · Answer 5 · 2017-01-24 22:55:52

1.6k

Views

How to define a covariant derivative on a smooth vector bundle using only an Ehresmann connection?

Published on 24 Jan 2017 - 22:55

score 1k · Answer 6 · 2026-03-25 13:56:53

1k

Views

Levi--Civita connection of a product metric

Published on 25 Mar 2026 - 13:56

score 1.1k · Answer 7 · 2017-02-02 11:02:09

1.1k

Views

The other trace of the curvature tensor

Published on 02 Feb 2017 - 11:02

score 298 · Answer 8 · 2017-02-11 23:09:18

298

Views

Expression of $R_{ijk}^s$ in terms of coefficients $\Gamma_{ij}^k$ of the Riemannian connection

Published on 11 Feb 2017 - 23:09

score 893 · Answer 9 · 2017-02-12 19:50:29

893

Views

Why the codifferential depends only on the connection (and not the metric)?

Published on 12 Feb 2017 - 19:50

score 9.1k · Answer 10 · 2017-02-15 07:21:22

9.1k

Views

What is the affine connection, and what is the intuition behind/for affine connection?

Published on 15 Feb 2017 - 7:21

score 51 · Answer 11 · 2017-02-15 23:17:01

51

Views

Are there always non-parallel bundle morphisms which preserve metricity?

Published on 15 Feb 2017 - 23:17

score 47 · Answer 12 · 2017-02-20 20:11:26

47

Views

Easy way to see that harmonicity depends only on the connection of the target?

Published on 20 Feb 2017 - 20:11

score 68 · Answer 13 · 2026-03-26 01:28:07

68

Views

Connections and principial bundles

Published on 26 Mar 2026 - 1:28

score 141 · Answer 14 · 2017-02-24 11:07:33

141

Views

Can we have a Metric manifold without a connection/covariant derivative?

Published on 24 Feb 2017 - 11:07

score 77 · Answer 15 · 2017-02-24 12:16:04

77

Views

Are there smooth manifolds that do not admit a connection?

Published on 24 Feb 2017 - 12:16

List Question

Affine connections: how to show that $\sum_{ij} x_i X_i(y_j)X_j = \sum_k X(y_k) X_k$?

For a vector bundle $\xi:E\to M$, why is Trace a parallel section of the bundle $End(\xi)^*$?

Do the Chern classes of a principal bundle depend on an embedding $G\hookrightarrow U(n)$?

Book/Slides/Videos about points-topology-manifold-charts-riemannian manifolds etc

How to define a covariant derivative on a smooth vector bundle using only an Ehresmann connection?

Levi--Civita connection of a product metric

The other trace of the curvature tensor

Expression of $R_{ijk}^s$ in terms of coefficients $\Gamma_{ij}^k$ of the Riemannian connection

Why the codifferential depends only on the connection (and not the metric)?

What is the affine connection, and what is the intuition behind/for affine connection?

Are there always non-parallel bundle morphisms which preserve metricity?

Easy way to see that harmonicity depends only on the connection of the target?

Connections and principial bundles

Can we have a Metric manifold without a connection/covariant derivative?

Are there smooth manifolds that do not admit a connection?

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