Question

$M$ complete, simply connected manifold with zero curvature $\Rightarrow M$ is globally isometric to $\mathbb{R}^n$

score 563 · Answer 1 · 2026-03-25 23:52:25

563

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$M$ complete, simply connected manifold with zero curvature $\Rightarrow M$ is globally isometric to $\mathbb{R}^n$

Published on 25 Mar 2026 - 23:52

score 673 · Answer 2 · 2019-12-12 15:34:56

673

Views

Calculate the Gaussian curvature of hyperbolic space

Published on 12 Dec 2019 - 15:34

score 160 · Answer 3 · 2026-03-25 23:19:15

160

Views

Idea about Einstein Manifold and vacuum Einstein field equation

Published on 25 Mar 2026 - 23:19

score 8.8k · Answer 4 · 2019-12-15 12:02:51

8.8k

Views

Gaussian and mean curvature of a sphere

Published on 15 Dec 2019 - 12:02

score 597 · Answer 5 · 2019-12-17 13:54:09

597

Views

The Gaussian and mean curvature of an implicit surface

Published on 17 Dec 2019 - 13:54

score 107 · Answer 6 · 2019-12-18 16:56:56

107

Views

Geodesics and curvature in cotangent bundle

Published on 18 Dec 2019 - 16:56

score 120 · Answer 7 · 2019-12-18 20:24:53

120

Views

explanation of first line in solution of question about curvature

Published on 18 Dec 2019 - 20:24

score 590 · Answer 8 · 2026-02-23 04:40:33

590

Views

Conformal invariance of Cotton tensor in dimension 3

Published on 23 Feb 2026 - 4:40

score 3.4k · Answer 9 · 2019-12-21 16:03:38

3.4k

Views

Torsion formula derivation

Published on 21 Dec 2019 - 16:03

score 203 · Answer 10 · 2019-12-28 19:04:20

203

Views

Filling in a missing detail in a Gauss-Bonnet problem

Published on 28 Dec 2019 - 19:04

score 71 · Answer 11 · 2026-03-25 16:12:38

71

Views

Maximize integral over a 3D knot - how to make my intuition rigorous?

Published on 25 Mar 2026 - 16:12

score 1.2k · Answer 12 · 2020-01-03 14:10:38

1.2k

Views

Ricci-flat vs Riemann-flat

Published on 03 Jan 2020 - 14:10

score 30 · Answer 13 · 2020-01-03 14:58:24

30

Views

Condition in the definition of the functions $E,$ $F$ and $G$ in Gauss's linear element formulas

Published on 03 Jan 2020 - 14:58

score 263 · Answer 14 · 2020-01-05 14:59:15

263

Views

Gaussian curvature of a surface which is equal to the $(x,y)$-plane outside a ball of radius $10$

Published on 05 Jan 2020 - 14:59

score 82 · Answer 15 · 2020-01-07 13:38:39

82

Views

Deducing the gradient of the functional $L(\gamma)=\int_0^1\|\gamma'(s)\|\ \mathrm ds$ is of the form $\nabla L(s)=-\kappa(s)\nu(s)$

Published on 07 Jan 2020 - 13:38

List Question

$M$ complete, simply connected manifold with zero curvature $\Rightarrow M$ is globally isometric to $\mathbb{R}^n$

Calculate the Gaussian curvature of hyperbolic space

Idea about Einstein Manifold and vacuum Einstein field equation

Gaussian and mean curvature of a sphere

The Gaussian and mean curvature of an implicit surface

Geodesics and curvature in cotangent bundle

explanation of first line in solution of question about curvature

Conformal invariance of Cotton tensor in dimension 3

Torsion formula derivation

Filling in a missing detail in a Gauss-Bonnet problem

Maximize integral over a 3D knot - how to make my intuition rigorous?

Ricci-flat vs Riemann-flat

Condition in the definition of the functions $E,$ $F$ and $G$ in Gauss's linear element formulas

Gaussian curvature of a surface which is equal to the $(x,y)$-plane outside a ball of radius $10$

Deducing the gradient of the functional $L(\gamma)=\int_0^1\|\gamma'(s)\|\ \mathrm ds$ is of the form $\nabla L(s)=-\kappa(s)\nu(s)$

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