List questions from differential-geometry

Published on 10 Apr 2026 - 7:19

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Worked examples of Lie derivatives

Published on 13 Apr 2026 - 6:52

67

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How can I prove that a systole of a close oriented hyperbolic surface S is a simple closed curve?

Published on 13 Apr 2026 - 21:55

225

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Prove by the integral definition that total curvature of lemniscate is $0$.

Published on 14 Apr 2026 - 12:06

52

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Worked examples of Lie derivative

Published on 14 Apr 2026 - 15:54

277

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Exponential map is smooth

Published on 14 Apr 2026 - 21:23

160

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In which degrees there exist non-decomposable elements in the exterior algebra?

Published on 09 Apr 2026 - 6:06

97

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Given a specific curve $\alpha(s)$, Prove that $\kappa(s) \geq 1/R$, where $\kappa(s)$ is the curvature of $\alpha$ at $s$.

Published on 16 Apr 2026 - 10:06

382

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Maurer Cartan $1$-form explanation of notation

Published on 09 Apr 2026 - 22:24

85

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How to generalize transversality condition?

Published on 11 Apr 2026 - 1:49

1.3k

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Gaussian curvature of surface

Published on 15 Apr 2026 - 8:40

1k

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Prove that the planar curve obtained by projecting $\alpha$ into its osculating plane at $P$ has the same curvature at $P$ as $\alpha$.

Published on 16 Apr 2026 - 15:09

101

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Book for manifolds that are used in scientific computation

Published on 28 Mar 2026 - 6:15

31

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Is Multi-dimensional arrays always enough information to describe a Tensor?

Published on 13 Apr 2026 - 18:19

430

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Does $d x^\mu=g^{\mu\nu} \partial_\nu$, or $\partial_\nu=g_{\nu \mu}dx^\mu$?

Published on 16 Apr 2026 - 11:31

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Parametric equations intuition

Worked examples of Lie derivatives

How can I prove that a systole of a close oriented hyperbolic surface S is a simple closed curve?

Prove by the integral definition that total curvature of lemniscate is $0$.

Worked examples of Lie derivative

Exponential map is smooth

In which degrees there exist non-decomposable elements in the exterior algebra?

Given a specific curve $\alpha(s)$, Prove that $\kappa(s) \geq 1/R$, where $\kappa(s)$ is the curvature of $\alpha$ at $s$.

Maurer Cartan $1$-form explanation of notation

How to generalize transversality condition?

Gaussian curvature of surface

Prove that the planar curve obtained by projecting $\alpha$ into its osculating plane at $P$ has the same curvature at $P$ as $\alpha$.

Book for manifolds that are used in scientific computation

Is Multi-dimensional arrays always enough information to describe a Tensor?

Does $d x^\mu=g^{\mu\nu} \partial_\nu$, or $\partial_\nu=g_{\nu \mu}dx^\mu$?

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