Question

How to obtain the metric tensor of a principal bundle total space given a connection (assuming it is metric compatible) in the total space?

score 76 · Answer 1 · 2015-05-13 20:24:31

76

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How to obtain the metric tensor of a principal bundle total space given a connection (assuming it is metric compatible) in the total space?

Published on 13 May 2015 - 20:24

score 118 · Answer 2 · 2026-02-23 01:04:24

118

Views

Cartan geometry on manifolds with boundary

Published on 23 Feb 2026 - 1:04

score 2.7k · Answer 3 · 2015-05-25 10:40:47

2.7k

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Classify sphere bundles over a sphere

Published on 25 May 2015 - 10:40

score 170 · Answer 4 · 2015-05-28 17:17:14

170

Views

Does naturality for characteristic classes imply the classifying space is universal for them?

Published on 28 May 2015 - 17:17

score 57 · Answer 5 · 2015-05-30 18:32:58

57

Views

Connection of a $G$-principal bundle as a section of a vector bundle?

Published on 30 May 2015 - 18:32

score 60 · Answer 6 · 2015-06-09 21:29:20

60

Views

Certain principle bundle structure on $\mathbb{R}^{n}\setminus \{0\}$

Published on 09 Jun 2015 - 21:29

score 204 · Answer 7 · 2026-03-25 19:10:28

204

Views

How to Induce a Metric on Homogeneous Space $G/H$ by the Metric from Bundle G

Published on 25 Mar 2026 - 19:10

score 1k · Answer 8 · 2015-06-16 19:04:28

1k

Views

The fundamental vector fields of a principal bundle are vertical.

Published on 16 Jun 2015 - 19:04

score 543 · Answer 9 · 2015-06-17 07:25:13

543

Views

Motivation for the name "vertical subspace" in the context of fiber bundles.

Published on 17 Jun 2015 - 7:25

score 409 · Answer 10 · 2015-06-17 17:19:36

409

Views

Applications of Principal Bundle Construction: Vague Question

Published on 17 Jun 2015 - 17:19

score 485 · Answer 11 · 2015-06-20 07:20:03

485

Views

A Lie Group Homomorphism $f:G\to H$ Induces a Functor from Principal $G$-Bundles to $H$-Bundles

Published on 20 Jun 2015 - 7:20

score 108 · Answer 12 · 2026-03-25 19:01:43

108

Views

Rigorously what is this integral?

Published on 25 Mar 2026 - 19:01

score 598 · Answer 13 · 2015-06-22 14:43:57

598

Views

To Reconcile Two Different Descriptions of the Dual Bundle

Published on 22 Jun 2015 - 14:43

score 504 · Answer 14 · 2026-03-25 20:35:01

504

Views

Quotient space of equivariant vector bundle.

Published on 25 Mar 2026 - 20:35

score 108 · Answer 15 · 2015-06-23 23:31:13

108

Views

Reduction to the special orthogonal group

Published on 23 Jun 2015 - 23:31

List Question

How to obtain the metric tensor of a principal bundle total space given a connection (assuming it is metric compatible) in the total space?

Cartan geometry on manifolds with boundary

Classify sphere bundles over a sphere

Does naturality for characteristic classes imply the classifying space is universal for them?

Connection of a $G$-principal bundle as a section of a vector bundle?

Certain principle bundle structure on $\mathbb{R}^{n}\setminus \{0\}$

How to Induce a Metric on Homogeneous Space $G/H$ by the Metric from Bundle G

The fundamental vector fields of a principal bundle are vertical.

Motivation for the name "vertical subspace" in the context of fiber bundles.

Applications of Principal Bundle Construction: Vague Question

A Lie Group Homomorphism $f:G\to H$ Induces a Functor from Principal $G$-Bundles to $H$-Bundles

Rigorously what is this integral?

To Reconcile Two Different Descriptions of the Dual Bundle

Quotient space of equivariant vector bundle.

Reduction to the special orthogonal group

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