List questions from curvature

Published on 30 Aug 2019 - 22:01

43

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Intrinsic curvature circular reasoning?

Published on 31 Aug 2019 - 23:05

1.2k

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Show that the torsion satisfies $\tau(s)=\frac{-\alpha'(s)\wedge\alpha''(s)\cdot\alpha'''(s)}{|\kappa(s)|^2}$

Published on 04 Sep 2019 - 15:11

803

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Determining a curvature by knowing the binormal vector

Published on 06 Sep 2019 - 19:23

1k

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Find curve given by its curvature, a point and and a tangent vector

Published on 25 Mar 2026 - 16:13

702

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Relation between simple closed curve with curvature smaller than radius circle

Published on 14 Sep 2019 - 2:38

998

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Calculating the curvature of product manifold $\mathbb{S}^2 \times \mathbb{R}$

Published on 18 Sep 2019 - 1:19

1.1k

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Curve whose signed curvature is $1 / (1 + s^2)$

Published on 21 Sep 2019 - 17:37

4.5k

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Proving the Frenet-Serret formulae

Published on 25 Mar 2026 - 3:00

430

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Can a manifold have zero curvature but non-zero torsion?

Published on 25 Sep 2019 - 12:52

544

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Do Carmo's question about Gauus aplication and planar points

Published on 26 Sep 2019 - 13:36

473

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Maximally symmetric space is completely determined by its constant scalar curvature

Published on 26 Mar 2026 - 3:12

317

Views

Two curvature formulas when equal arc-length

Published on 11 Mar 2014 - 23:54

1.2k

Views

Total/Gaussian curvature is intrinsic, yet mean curvature is extrinsic, why?

Published on 18 Mar 2014 - 14:00

811

Views

Cartan formalism calculation

Published on 19 Mar 2014 - 19:59

List Question

Intrinsic curvature calculation

Intrinsic curvature circular reasoning?

Show that the torsion satisfies $\tau(s)=\frac{-\alpha'(s)\wedge\alpha''(s)\cdot\alpha'''(s)}{|\kappa(s)|^2}$

Determining a curvature by knowing the binormal vector

Find curve given by its curvature, a point and and a tangent vector

Relation between simple closed curve with curvature smaller than radius circle

Calculating the curvature of product manifold $\mathbb{S}^2 \times \mathbb{R}$

Curve whose signed curvature is $1 / (1 + s^2)$

Proving the Frenet-Serret formulae

Can a manifold have zero curvature but non-zero torsion?

Do Carmo's question about Gauus aplication and planar points

Maximally symmetric space is completely determined by its constant scalar curvature

Two curvature formulas when equal arc-length

Total/Gaussian curvature is intrinsic, yet mean curvature is extrinsic, why?

Cartan formalism calculation

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