Question

Let $M$ be a Riemannian manifold. When does the Laplace-Beltrami operator differ from the trace of the Hessian?

score 2.1k · Answer 1 · 2026-04-14 22:02:47

2.1k

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Let $M$ be a Riemannian manifold. When does the Laplace-Beltrami operator differ from the trace of the Hessian?

Published on 14 Apr 2026 - 22:02

score 2.7k · Answer 2 · 2026-04-13 03:07:49

2.7k

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Every compact manifold is geodesically complete

Published on 13 Apr 2026 - 3:07

score 282 · Answer 3 · 2026-04-15 15:34:45

282

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All Covariant Derivatures of Curvature Tensor Being Zero

Published on 15 Apr 2026 - 15:34

score 657 · Answer 4 · 2026-04-12 03:12:42

657

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Prove Levi-Civita connection is torsion free

Published on 12 Apr 2026 - 3:12

score 91 · Answer 5 · 2026-04-14 19:40:56

91

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Prove that $\mathbb{R}^m$ is flat

Published on 14 Apr 2026 - 19:40

score 43 · Answer 6 · 2026-04-17 11:46:56

43

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Normal vector of cylinderical graph

Published on 17 Apr 2026 - 11:46

score 36 · Answer 7 · 2026-04-16 02:22:04

36

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Hypersphere constant radius in lower dimensions

Published on 16 Apr 2026 - 2:22

score 1.5k · Answer 8 · 2026-04-10 10:25:27

1.5k

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The Sphere Does Not Admit a Metric Isometry into a Euclidean Space.

Published on 10 Apr 2026 - 10:25

score 726 · Answer 9 · 2026-04-13 17:42:39

726

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Contraction of a tensor

Published on 13 Apr 2026 - 17:42

score 322 · Answer 10 · 2026-04-15 21:50:20

322

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Exercise 8.4(a) of Do Carmo, Riemannian Geometry

Published on 15 Apr 2026 - 21:50

score 105 · Answer 11 · 2026-04-13 00:49:10

105

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Riemann Curvature: How to proof the identical relation and why ${R_{1212}}$ is only independent variant about Riemann Curvature?

Published on 13 Apr 2026 - 0:49

score 1k · Answer 12 · 2026-04-08 23:06:55

1k

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Trying to understand a proof of the existence of isothermal coordinates for $2$-dimensional Riemannian manifolds

Published on 08 Apr 2026 - 23:06

score 751 · Answer 13 · 2026-05-11 01:37:38

751

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Distance function on the complex projective space

Published on 11 May 2026 - 1:37

score 833 · Answer 14 · 2026-05-05 07:47:49

833

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Euler Characteristic of fiber bundle using Differential Geometry

Published on 05 May 2026 - 7:47

score 277 · Answer 15 · 2026-04-15 10:23:29

277

Views

Counterexample to Gunther Theorem when assuming only a Ricci curvature upper bound

Published on 15 Apr 2026 - 10:23

List Question

Let $M$ be a Riemannian manifold. When does the Laplace-Beltrami operator differ from the trace of the Hessian?

Every compact manifold is geodesically complete

All Covariant Derivatures of Curvature Tensor Being Zero

Prove Levi-Civita connection is torsion free

Prove that $\mathbb{R}^m$ is flat

Normal vector of cylinderical graph

Hypersphere constant radius in lower dimensions

The Sphere Does Not Admit a Metric Isometry into a Euclidean Space.

Contraction of a tensor

Exercise 8.4(a) of Do Carmo, Riemannian Geometry

Riemann Curvature: How to proof the identical relation and why ${R_{1212}}$ is only independent variant about Riemann Curvature?

Trying to understand a proof of the existence of isothermal coordinates for $2$-dimensional Riemannian manifolds

Distance function on the complex projective space

Euler Characteristic of fiber bundle using Differential Geometry

Counterexample to Gunther Theorem when assuming only a Ricci curvature upper bound

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