Question

Is the tangent bundle of a $S^2$ flat?

score 785 · Answer 1 · 2026-04-12 00:54:46

785

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Is the tangent bundle of a $S^2$ flat?

Published on 12 Apr 2026 - 0:54

score 1.7k · Answer 2 · 2026-04-11 21:02:02

1.7k

Views

Covariant derivative and the product rule

Published on 11 Apr 2026 - 21:02

score 492 · Answer 3 · 2026-04-14 02:52:30

492

Views

Covariant derivative and orthogonal projection

Published on 14 Apr 2026 - 2:52

score 149 · Answer 4 · 2026-04-15 03:50:36

149

Views

About the antisymmetry of the curvature matrix in vector bundle

Published on 15 Apr 2026 - 3:50

score 197 · Answer 5 · 2026-05-10 12:42:42

197

Views

Exterior Covariant Derivative - Proof of Structure Equation for general r-form

Published on 10 May 2026 - 12:42

score 892 · Answer 6 · 2026-04-09 08:48:32

892

Views

Parallel transport in two different polar coordinates

Published on 09 Apr 2026 - 8:48

score 449 · Answer 7 · 2026-04-12 22:23:40

449

Views

Proof of the formula for the exterior derivative in terms of the covariant derivative.

Published on 12 Apr 2026 - 22:23

score 92 · Answer 8 · 2026-04-12 19:57:19

92

Views

How to derive the Leibniz rule from this definition of a connection of a vector bundle?

Published on 12 Apr 2026 - 19:57

score 91 · Answer 9 · 2026-05-10 12:40:44

91

Views

How to arrive at frame bundle objects from chart calculation on the base manifold

Published on 10 May 2026 - 12:40

score 173 · Answer 10 · 2026-05-10 13:50:09

173

Views

Consider symplectic vector fields $X,Y$ and a symplectic connection $\nabla$. Is $\nabla_{X}Y$ symplectic?

Published on 10 May 2026 - 13:50

score 83 · Answer 11 · 2026-04-17 03:58:48

83

Views

Sign issue when computing identity involving curvature for a connection $\nabla + A$ of a bundle $E\to M$

Published on 17 Apr 2026 - 3:58

score 126 · Answer 12 · 2026-04-14 18:08:23

126

Views

Surjective geodesic exponential map on a Lie group

Published on 14 Apr 2026 - 18:08

score 67 · Answer 13 · 2026-04-12 00:04:56

67

Views

Induced metric from Euclidean space

Published on 12 Apr 2026 - 0:04

score 62 · Answer 14 · 2026-04-29 12:54:45

62

Views

Why is the interpolation between two connections related via a gauge transformation still a connection?

Published on 29 Apr 2026 - 12:54

score 94 · Answer 15 · 2026-04-09 09:53:09

94

Views

A question about holomorphic structure in Atiyah Bott's paper.

Published on 09 Apr 2026 - 9:53

List Question

Is the tangent bundle of a $S^2$ flat?

Covariant derivative and the product rule

Covariant derivative and orthogonal projection

About the antisymmetry of the curvature matrix in vector bundle

Exterior Covariant Derivative - Proof of Structure Equation for general r-form

Parallel transport in two different polar coordinates

Proof of the formula for the exterior derivative in terms of the covariant derivative.

How to derive the Leibniz rule from this definition of a connection of a vector bundle?

How to arrive at frame bundle objects from chart calculation on the base manifold

Consider symplectic vector fields $X,Y$ and a symplectic connection $\nabla$. Is $\nabla_{X}Y$ symplectic?

Sign issue when computing identity involving curvature for a connection $\nabla + A$ of a bundle $E\to M$

Surjective geodesic exponential map on a Lie group

Induced metric from Euclidean space

Why is the interpolation between two connections related via a gauge transformation still a connection?

A question about holomorphic structure in Atiyah Bott's paper.

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