Question

Why can the mean curvature vector be expressed by a limit of a line integral over closed curves?

score 398 · Answer 1 · 2026-03-25 19:06:20

398

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Why can the mean curvature vector be expressed by a limit of a line integral over closed curves?

Published on 25 Mar 2026 - 19:06

score 2.3k · Answer 2 · 2026-03-29 03:35:44

2.3k

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Calculating Levi-Civita Connection and Curvature for Euclidean Metric

Published on 29 Mar 2026 - 3:35

score 125 · Answer 3 · 2017-05-02 18:17:52

125

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Determining parametrization of curve from its acceleration

Published on 02 May 2017 - 18:17

score 55 · Answer 4 · 2017-05-03 02:27:54

55

Views

Gauss curvature of points that are covered by a certain parametrization

Published on 03 May 2017 - 2:27

score 131 · Answer 5 · 2017-05-04 11:32:50

131

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Problem with Gauss-Codazzi compatibility equations in intrinsic curvilinear coordinates

Published on 04 May 2017 - 11:32

score 1.2k · Answer 6 · 2017-05-05 02:36:05

1.2k

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Gauss–Kronecker curvature and Gauss curvature

Published on 05 May 2017 - 2:36

score 196 · Answer 7 · 2017-05-06 00:04:58

196

Views

What should be minimized in order to best approximate a curve?

Published on 06 May 2017 - 0:04

score 1.8k · Answer 8 · 2017-05-06 08:25:08

1.8k

Views

Why is the variation of a Christoffel symbol a tensor

Published on 06 May 2017 - 8:25

score 100 · Answer 9 · 2017-05-06 12:55:39

100

Views

Curvature symmetries in local coordinates

Published on 06 May 2017 - 12:55

score 587 · Answer 10 · 2017-05-07 21:36:27

587

Views

Curvature of Conformally Equivalent/Flat metrics

Published on 07 May 2017 - 21:36

score 295 · Answer 11 · 2017-05-07 22:45:19

295

Views

Variation on Gauss-Bonnet Theorem (disjoint discs)

Published on 07 May 2017 - 22:45

score 826 · Answer 12 · 2017-05-10 14:12:00

826

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$S\subset\mathbb{R}^3$ compact, orientable, not a sphere $\Rightarrow K$ has positive and negative values

Published on 10 May 2017 - 14:12

score 2.2k · Answer 13 · 2026-03-29 12:12:06

2.2k

Views

Geodesic curvature and projection onto the tangent plane

Published on 29 Mar 2026 - 12:12

score 2.2k · Answer 14 · 2017-05-10 21:06:27

2.2k

Views

Orthogonal differentiable family of curves

Published on 10 May 2017 - 21:06

score 608 · Answer 15 · 2017-05-11 18:33:30

608

Views

Why does a surface of uniform negative curvature have infinite area?

Published on 11 May 2017 - 18:33

List Question

Why can the mean curvature vector be expressed by a limit of a line integral over closed curves?

Calculating Levi-Civita Connection and Curvature for Euclidean Metric

Determining parametrization of curve from its acceleration

Gauss curvature of points that are covered by a certain parametrization

Problem with Gauss-Codazzi compatibility equations in intrinsic curvilinear coordinates

Gauss–Kronecker curvature and Gauss curvature

What should be minimized in order to best approximate a curve?

Why is the variation of a Christoffel symbol a tensor

Curvature symmetries in local coordinates

Curvature of Conformally Equivalent/Flat metrics

Variation on Gauss-Bonnet Theorem (disjoint discs)

$S\subset\mathbb{R}^3$ compact, orientable, not a sphere $\Rightarrow K$ has positive and negative values

Geodesic curvature and projection onto the tangent plane

Orthogonal differentiable family of curves

Why does a surface of uniform negative curvature have infinite area?

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