List questions from principal-bundles

Published on 08 Oct 2014 - 21:38

66

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Let $\pi: E \to M$ a vector bundle. Is $E$ a direct summnad of $M\times\mathbb{R}^{d}$, for some $d$?

Published on 15 Oct 2014 - 21:20

301

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Principal bundle map is fiber homeomorphism

Published on 07 Nov 2014 - 9:57

538

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Reference for principal bundles and related concepts

Published on 12 Nov 2014 - 22:42

168

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This result holds in general or just for vector bundles?

Published on 15 Nov 2014 - 13:36

158

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Contraction of second exterior covariant derivative with metric

Published on 25 Mar 2026 - 9:39

730

Views

Lifting Riemannian metrics on principal bundles

Published on 02 Dec 2014 - 10:33

5k

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$M \times N$ orientable if and only if $M, N$ orientable

Published on 07 Dec 2014 - 5:37

93

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What is the principal bundle structure of $O(n)$?

Published on 25 Mar 2026 - 12:19

52

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Can I always find a principal bundle so that I can build my given fibre bundle on it?

Published on 03 Oct 2019 - 18:49

71

Views

lifting a flat $G/H$ connection to a $G$ connection

Published on 05 Oct 2019 - 18:25

51

Views

Classical groups, representations, and associate bundles.

Published on 05 Oct 2019 - 23:37

92

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Connection on principle bundle

Published on 25 Mar 2026 - 7:46

261

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Covariant derivative on the base space

Published on 13 Oct 2019 - 15:47

399

Views

Definition of principal $G$-bundle might be missing details or have implicit assumptions on actions on each trivializing open set

Published on 16 Oct 2019 - 8:01

List Question

Principal $\mathrm{SL}_n$-bundles

Let $\pi: E \to M$ a vector bundle. Is $E$ a direct summnad of $M\times\mathbb{R}^{d}$, for some $d$?

Principal bundle map is fiber homeomorphism

Reference for principal bundles and related concepts

This result holds in general or just for vector bundles?

Contraction of second exterior covariant derivative with metric

Lifting Riemannian metrics on principal bundles

$M \times N$ orientable if and only if $M, N$ orientable

What is the principal bundle structure of $O(n)$?

Can I always find a principal bundle so that I can build my given fibre bundle on it?

lifting a flat $G/H$ connection to a $G$ connection

Classical groups, representations, and associate bundles.

Connection on principle bundle

Covariant derivative on the base space

Definition of principal $G$-bundle might be missing details or have implicit assumptions on actions on each trivializing open set

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