List questions from riemannian-geometry

Published on 20 Nov 2018 - 14:16

311

Views

Two flat tori are isometric iff their lattices are isometric?

Published on 20 Nov 2018 - 19:01

315

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Homogeneous polynomial on unit sphere.

Published on 21 Nov 2018 - 13:23

326

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Exponential map on the Fisher manifold for exponential family distribution

Published on 22 Mar 2026 - 4:44

101

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A relation between left-invariant vector fields

Published on 26 Mar 2026 - 6:17

215

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Show that any affine connection $\nabla$ on $\mathbb{R}^n$ is of the form $\nabla=D+\Gamma$.

Published on 25 Mar 2026 - 15:52

269

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Is velocity field extendible to a vector field on the whole manifold?

Published on 26 Mar 2026 - 8:03

157

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Concrete interpretation of parallelism of a vector field along a curve

Published on 26 Mar 2026 - 6:21

77

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If two Riemannian manifolds are isometric as metric spaces, must they be isometric as Riemannian manifolds?

Published on 24 Nov 2018 - 5:09

492

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Hyperbolic Geometry: Representation of the metric in a chart

Published on 26 Mar 2026 - 4:31

27

Views

Help to understand that $x\left( z\right) ={Re}\int_{z_{0}}^{z}\phi \left( \xi \right) d\xi $ is well defined

Published on 26 Nov 2018 - 1:35

95

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Cogeodesic flow on compact manifold has compact leaves and manifold

Published on 26 Nov 2018 - 1:59

61

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Is the "immersed proper" hypothesis necessary in Half-space Theorem?

Published on 25 Mar 2026 - 3:22

43

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Is there such a thing as a "most parallel" vector on a curved manifold?

Published on 27 Nov 2018 - 17:40

99

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Is there any non-complete metric on $\Bbb R^2$?

Published on 28 Nov 2018 - 5:30

List Question

Smooth and Riemannian metrics?

Two flat tori are isometric iff their lattices are isometric?

Homogeneous polynomial on unit sphere.

Exponential map on the Fisher manifold for exponential family distribution

A relation between left-invariant vector fields

Show that any affine connection $\nabla$ on $\mathbb{R}^n$ is of the form $\nabla=D+\Gamma$.

Is velocity field extendible to a vector field on the whole manifold?

Concrete interpretation of parallelism of a vector field along a curve

If two Riemannian manifolds are isometric as metric spaces, must they be isometric as Riemannian manifolds?

Hyperbolic Geometry: Representation of the metric in a chart

Help to understand that $x\left( z\right) ={Re}\int_{z_{0}}^{z}\phi \left( \xi \right) d\xi $ is well defined

Cogeodesic flow on compact manifold has compact leaves and manifold

Is the "immersed proper" hypothesis necessary in Half-space Theorem?

Is there such a thing as a "most parallel" vector on a curved manifold?

Is there any non-complete metric on $\Bbb R^2$?

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