Question

Simply-connected manifold of constant sectional curvature can be isometrically immersed in model space

score 235 · Answer 1 · 2021-12-11 14:37:13

235

Views

Simply-connected manifold of constant sectional curvature can be isometrically immersed in model space

Published on 11 Dec 2021 - 14:37

score 223 · Answer 2 · 2021-12-12 08:08:19

223

Views

Geodesic equation parametrized by arc length

Published on 12 Dec 2021 - 8:08

score 85 · Answer 3 · 2026-02-24 05:37:27

85

Views

References to understand $\frac{d}{dt} d(x,y) = \frac 12 \inf \int_\gamma g'(S,S) ds$, for flows on manifolds

Published on 24 Feb 2026 - 5:37

score 631 · Answer 4 · 2026-03-29 04:34:35

631

Views

Show that $V^{\mu} = (\cos\phi, -\cot\theta \sin\phi)$ is a Killing's vector on the 2-sphere.

Published on 29 Mar 2026 - 4:34

score 307 · Answer 5 · 2021-12-18 15:54:54

307

Views

Geodesic crosses every parallel in a surface of revolution.

Published on 18 Dec 2021 - 15:54

score 313 · Answer 6 · 2021-12-19 17:26:48

313

Views

If $M \subset \mathbb{R}^3$ is connected and every geodesic is planar, then $M$ is contained in a plane or a sphere

Published on 19 Dec 2021 - 17:26

score 253 · Answer 7 · 2026-03-27 04:16:40

253

Views

Can an incomplete geodesic intersect a point infinitely many times?

Published on 27 Mar 2026 - 4:16

score 96 · Answer 8 · 2021-12-21 23:27:14

96

Views

Curvature and geodesic of $M = \mathbb{R}\times \mathbb{R}_{>0}$ with metric $ds^2 = dx^2 + ydy^2$

Published on 21 Dec 2021 - 23:27

score 379 · Answer 9 · 2021-12-24 15:48:39

379

Views

A convergent sequence of geodesics converges to a geodesic

Published on 24 Dec 2021 - 15:48

score 67 · Answer 10 · 2026-02-23 10:15:01

67

Views

Density associated with Wasserstein geodesic

Published on 23 Feb 2026 - 10:15

score 87 · Answer 11 · 2026-03-30 10:13:18

87

Views

Chern's Lectures on Differential Geometry, 5.2, torsion free connection and curvature tensor

Published on 30 Mar 2026 - 10:13

score 86 · Answer 12 · 2021-12-29 15:49:13

86

Views

Geodesic calculation using Euler-Lagrange's Equation

Published on 29 Dec 2021 - 15:49

score 188 · Answer 13 · 2022-01-04 15:49:53

188

Views

Do Equidistant points form a Geodesic in the Torus?

Published on 04 Jan 2022 - 15:49

score 41 · Answer 14 · 2022-01-09 22:53:57

41

Views

How can we let paths in Riemannian manifold flow towards being a geodesic?

Published on 09 Jan 2022 - 22:53

score 189 · Answer 15 · 2022-01-16 21:56:17

189

Views

How can I find the geodesics on the cylinder $x^2 + y^2 = 1$?

Published on 16 Jan 2022 - 21:56

List Question

Simply-connected manifold of constant sectional curvature can be isometrically immersed in model space

Geodesic equation parametrized by arc length

References to understand $\frac{d}{dt} d(x,y) = \frac 12 \inf \int_\gamma g'(S,S) ds$, for flows on manifolds

Show that $V^{\mu} = (\cos\phi, -\cot\theta \sin\phi)$ is a Killing's vector on the 2-sphere.

Geodesic crosses every parallel in a surface of revolution.

If $M \subset \mathbb{R}^3$ is connected and every geodesic is planar, then $M$ is contained in a plane or a sphere

Can an incomplete geodesic intersect a point infinitely many times?

Curvature and geodesic of $M = \mathbb{R}\times \mathbb{R}_{>0}$ with metric $ds^2 = dx^2 + ydy^2$

A convergent sequence of geodesics converges to a geodesic

Density associated with Wasserstein geodesic

Chern's Lectures on Differential Geometry, 5.2, torsion free connection and curvature tensor

Geodesic calculation using Euler-Lagrange's Equation

Do Equidistant points form a Geodesic in the Torus?

How can we let paths in Riemannian manifold flow towards being a geodesic?

How can I find the geodesics on the cylinder $x^2 + y^2 = 1$?

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