Question

Most succinct proof of the uniqueness and existence of the Levi-Civita connection.

score 1.8k · Answer 1 · 2012-05-04 13:24:23

1.8k

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Most succinct proof of the uniqueness and existence of the Levi-Civita connection.

Published on 04 May 2012 - 13:24

score 3.6k · Answer 2 · 2012-11-12 17:10:19

3.6k

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How to define a connection on the dual bundle?

Published on 12 Nov 2012 - 17:10

score 169 · Answer 3 · 2012-11-26 18:19:01

169

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Regarding the definition of connections (covariant derivatives)

Published on 26 Nov 2012 - 18:19

score 23.3k · Answer 4 · 2012-11-30 20:32:16

23.3k

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Prove that Christoffel symbols transformation law via the metric tensor

Published on 30 Nov 2012 - 20:32

score 442 · Answer 5 · 2026-03-27 09:57:05

442

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Special Kähler manifolds

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score 526 · Answer 6 · 2026-03-27 09:48:20

526

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Flat torsionfree connection in Kähler manifold

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score 4k · Answer 7 · 2026-03-26 04:32:37

4k

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Does the Levi-Civita connection determine the metric?

Published on 26 Mar 2026 - 4:32

score 714 · Answer 8 · 2026-03-28 22:28:23

714

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do Carmo Riemannian Geometry Exercise 2.3: definition of $\nabla$ for an immersion

Published on 28 Mar 2026 - 22:28

score 856 · Answer 9 · 2026-03-28 22:31:06

856

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do Carmo Riemannian Geometry Exercise 2.3: definition of $\nabla$ for an immersion - Part II

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score 134 · Answer 10 · 2020-08-11 11:24:30

134

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Relationship between fiber volume form on the sphere bundle and connection forms on the frame bundle

Published on 11 Aug 2020 - 11:24

score 185 · Answer 11 · 2020-08-19 17:53:34

185

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How is the wedge product in the Bianchi identity for torsion defined?

Published on 19 Aug 2020 - 17:53

score 193 · Answer 12 · 2026-03-26 06:34:43

193

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Is torsion-free affine connection not unique, but there is only one that is compatible with the metric?

Published on 26 Mar 2026 - 6:34

score 252 · Answer 13 · 2020-08-26 09:30:35

252

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Riemannian connection is flat iff there exists a Euclidean coordinate system

Published on 26 Aug 2020 - 9:30

score 466 · Answer 14 · 2020-08-29 04:54:00

466

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Published on 29 Aug 2020 - 4:54

score 365 · Answer 15 · 2026-03-26 22:51:53

365

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Understanding distance function on Riemannian Manifold

Published on 26 Mar 2026 - 22:51

List Question

Most succinct proof of the uniqueness and existence of the Levi-Civita connection.

How to define a connection on the dual bundle?

Regarding the definition of connections (covariant derivatives)

Prove that Christoffel symbols transformation law via the metric tensor

Special Kähler manifolds

Flat torsionfree connection in Kähler manifold

Does the Levi-Civita connection determine the metric?

do Carmo Riemannian Geometry Exercise 2.3: definition of $\nabla$ for an immersion

do Carmo Riemannian Geometry Exercise 2.3: definition of $\nabla$ for an immersion - Part II

Relationship between fiber volume form on the sphere bundle and connection forms on the frame bundle

How is the wedge product in the Bianchi identity for torsion defined?

Is torsion-free affine connection not unique, but there is only one that is compatible with the metric?

Riemannian connection is flat iff there exists a Euclidean coordinate system

Chain rule for covariant Hessian when the diffeomorphism is not an isometry

Understanding distance function on Riemannian Manifold

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