Question

Intuition behind curvature 2-forms

score 259 · Answer 1 · 2026-03-26 08:12:01

259

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Intuition behind curvature 2-forms

Published on 26 Mar 2026 - 8:12

score 53 · Answer 2 · 2023-08-19 00:14:46

53

Views

Gauß curvature of semi-riemannian hypersurfaces in $\mathbb{R}^3$

Published on 19 Aug 2023 - 0:14

score 82 · Answer 3 · 2023-08-19 19:26:41

82

Views

Identity for coefficient functions of Riemann Curvature Tensor.

Published on 19 Aug 2023 - 19:26

score 37 · Answer 4 · 2026-03-28 16:58:07

37

Views

Estimating mean curvature of a surface by two perpendicular curves of the surface

Published on 28 Mar 2026 - 16:58

score 120 · Answer 5 · 2023-08-20 15:36:47

120

Views

Ricci tensor and christoffel-symbols

Published on 20 Aug 2023 - 15:36

score 127 · Answer 6 · 2023-08-20 19:16:50

127

Views

The principal directions of curvature of the saddle surface z = xy

Published on 20 Aug 2023 - 19:16

score 48 · Answer 7 · 2026-03-26 08:07:29

48

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How does $\partial_\mu$ act on $A_\nu$ in the local structure equation for a curvature 2-form written in coordinates?

Published on 26 Mar 2026 - 8:07

score 605 · Answer 8 · 2023-08-22 18:34:04

605

Views

Intuition for the inverse Hessian matrix

Published on 22 Aug 2023 - 18:34

score 30 · Answer 9 · 2023-08-23 13:21:25

30

Views

Second Fundamental Form of Hypersurface Normal to Predefined Vector Field

Published on 23 Aug 2023 - 13:21

score 48 · Answer 10 · 2023-08-29 10:46:57

48

Views

Why is $R_p:T_pM\times T_pM \to \operatorname{Hom}(E_p,E_p)?$

Published on 29 Aug 2023 - 10:46

score 37 · Answer 11 · 2023-09-01 06:12:54

37

Views

Which formula does it use here to get the curvature?

Published on 01 Sep 2023 - 6:12

score 91 · Answer 12 · 2023-09-09 12:34:49

91

Views

Define $\langle,\rangle_{(x,y)} = dx\otimes dx + h(x)^2dy\otimes dy.$ Compute the Gaussian curvature of $\mathbb{R}^2$ with this metric.

Published on 09 Sep 2023 - 12:34

score 153 · Answer 13 · 2023-09-24 13:56:46

153

Views

What is the sectional curvature of this explicitely given n-dimensional submanifold of R^(n+1)?

Published on 24 Sep 2023 - 13:56

score 75 · Answer 14 · 2023-09-25 02:32:14

75

Views

Curvature at $t=0$ of epicycloid (parametrization included in body of question)

Published on 25 Sep 2023 - 2:32

score 40 · Answer 15 · 2023-09-28 08:22:06

40

Views

How to show that there must be a point on a compact smooth torus in $ \mathbb{R}^3 $ with positive or negative Gauss curvature?

Published on 28 Sep 2023 - 8:22

List Question

Intuition behind curvature 2-forms

Gauß curvature of semi-riemannian hypersurfaces in $\mathbb{R}^3$

Identity for coefficient functions of Riemann Curvature Tensor.

Estimating mean curvature of a surface by two perpendicular curves of the surface

Ricci tensor and christoffel-symbols

The principal directions of curvature of the saddle surface z = xy

How does $\partial_\mu$ act on $A_\nu$ in the local structure equation for a curvature 2-form written in coordinates?

Intuition for the inverse Hessian matrix

Second Fundamental Form of Hypersurface Normal to Predefined Vector Field

Why is $R_p:T_pM\times T_pM \to \operatorname{Hom}(E_p,E_p)?$

Which formula does it use here to get the curvature?

Define $\langle,\rangle_{(x,y)} = dx\otimes dx + h(x)^2dy\otimes dy.$ Compute the Gaussian curvature of $\mathbb{R}^2$ with this metric.

What is the sectional curvature of this explicitely given n-dimensional submanifold of R^(n+1)?

Curvature at $t=0$ of epicycloid (parametrization included in body of question)

How to show that there must be a point on a compact smooth torus in $ \mathbb{R}^3 $ with positive or negative Gauss curvature?

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