List questions from differential-geometry

Published on 25 Mar 2026 - 14:09

252

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does a proper variation through geodesics keep the length of geodesic fixed?

Published on 25 Mar 2026 - 14:03

1.5k

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Why do I care that smooth vector fields over a smooth manifold have a Lie algebra?

Published on 26 Mar 2026 - 1:16

298

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How is the generalised momentum a covector?

Published on 25 Mar 2026 - 9:15

146

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Connected semi-riemannian manifold is an Einstein manifold.

Published on 25 Mar 2026 - 20:56

38

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Geodesics on subsets of manifolds defined by a Euclidean coordinate system

Published on 25 Mar 2026 - 1:26

73

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Prove that there exist a point $p\in S^2$ such that $f(p)=\pm p$ for $f:S^2\to S^2$ a smooth function.

Published on 30 Apr 2018 - 18:46

208

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Check or falsify: there is a $C^\infty$ surjective map $S^1 \to S^1 \times S^1$.

Published on 26 Mar 2026 - 20:44

280

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About the pullback of a $1$-form

Published on 26 Mar 2026 - 6:05

730

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Riemannian metric and geodesics on a cone

Published on 25 Mar 2026 - 15:54

45

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Show that each two normal lines near a point with non zero curvature of a curve with arc length parametrization do intersect.

Published on 01 May 2018 - 20:45

100

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Step of the proof that $\mathbb{RP}^{3} \cong SO(3)$

Published on 24 Mar 2026 - 23:45

230

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Uniqueness of totally geodesic submanifold with a given tangent space

Published on 25 Mar 2026 - 1:27

1.1k

Views

Tangent bundle $TM$ is a submanifold of $\mathbb{R}^{2n}$

Published on 25 Mar 2026 - 1:16

635

Views

Vector fields on $S^3$

Published on 25 Mar 2026 - 18:14

List Question

A cohomology or homology associated to a Riemannian manifold or a dynamical system

does a proper variation through geodesics keep the length of geodesic fixed?

Why do I care that smooth vector fields over a smooth manifold have a Lie algebra?

How is the generalised momentum a covector?

Connected semi-riemannian manifold is an Einstein manifold.

Geodesics on subsets of manifolds defined by a Euclidean coordinate system

Prove that there exist a point $p\in S^2$ such that $f(p)=\pm p$ for $f:S^2\to S^2$ a smooth function.

Check or falsify: there is a $C^\infty$ surjective map $S^1 \to S^1 \times S^1$.

About the pullback of a $1$-form

Riemannian metric and geodesics on a cone

Show that each two normal lines near a point with non zero curvature of a curve with arc length parametrization do intersect.

Step of the proof that $\mathbb{RP}^{3} \cong SO(3)$

Uniqueness of totally geodesic submanifold with a given tangent space

Tangent bundle $TM$ is a submanifold of $\mathbb{R}^{2n}$

Vector fields on $S^3$

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