List questions from curvature

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How to show $g^{ij}g^{kl}h_{ik}h_{jl}=\frac{(g^{ij}h_{ij})^2}{n} \Rightarrow \text{it is a round sphere}$?

Published on 12 Mar 2017 - 2:45

227

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Ricci curvature of the $n$-ball

Published on 12 Mar 2017 - 20:26

1.6k

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Curvature of a regular not necessarily unit speed curve

Published on 13 Mar 2017 - 13:38

50

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Mean curvature and inner radius

Published on 13 Mar 2017 - 21:15

52

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Arc length parameterization and collinearity

Published on 14 Mar 2017 - 8:19

2.4k

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Constant curvature riemann manifold

Published on 14 Mar 2017 - 10:10

165

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Cartan's proof of the determination of the metric by means of curvature

Published on 14 Mar 2017 - 20:49

1.1k

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Properties of Frenet Curve

Published on 25 Mar 2026 - 6:05

596

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Second Fundamental Form of Hypersurface

Published on 15 Mar 2017 - 20:48

2.1k

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Curvature and Torsion in terms of Geodesic Curvature

Published on 27 Mar 2026 - 1:47

352

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Prove that $g^{jm}\nabla_i\mathrm{R}_{jklm} = \nabla_i(g^{jm}\mathrm{R}_{jklm}) = \nabla_i\mathrm{R}_{kl}$

Published on 17 Mar 2017 - 21:57

422

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Class of Surfaces of revolution

Published on 19 Mar 2017 - 14:00

2.4k

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An Einstein manifold in dimension 3 has a constant sectional curvature.

Published on 19 Mar 2017 - 17:13

274

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Modified Willmore energy and surfaces with infinitesimally narrow necks

Published on 20 Mar 2017 - 17:18

275

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Proving 2 things about Frenet Curves

Published on 25 Mar 2026 - 6:00

List Question

How to show $g^{ij}g^{kl}h_{ik}h_{jl}=\frac{(g^{ij}h_{ij})^2}{n} \Rightarrow \text{it is a round sphere}$?

Ricci curvature of the $n$-ball

Curvature of a regular not necessarily unit speed curve

Mean curvature and inner radius

Arc length parameterization and collinearity

Constant curvature riemann manifold

Cartan's proof of the determination of the metric by means of curvature

Properties of Frenet Curve

Second Fundamental Form of Hypersurface

Curvature and Torsion in terms of Geodesic Curvature

Prove that $g^{jm}\nabla_i\mathrm{R}_{jklm} = \nabla_i(g^{jm}\mathrm{R}_{jklm}) = \nabla_i\mathrm{R}_{kl}$

Class of Surfaces of revolution

An Einstein manifold in dimension 3 has a constant sectional curvature.

Modified Willmore energy and surfaces with infinitesimally narrow necks

Proving 2 things about Frenet Curves

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