Question

An intuitive question about the metric $d(\cdot,\cdot)$ on a complete Riemannian manifold

score 122 · Answer 1 · 2016-04-16 18:07:26

122

Views

An intuitive question about the metric $d(\cdot,\cdot)$ on a complete Riemannian manifold

Published on 16 Apr 2016 - 18:07

score 61 · Answer 2 · 2016-04-19 04:37:09

61

Views

Show that exist a unique field $G$ on $TM$ whose paths are of the form $t\to (\gamma(t),\gamma'(t))$, where $\gamma$ is a geodesic on $M$.

Published on 19 Apr 2016 - 4:37

score 22 · Answer 3 · 2016-04-19 05:05:59

22

Views

Let $\alpha, \beta:I\to M$, two geodesic. If exist a number $a\in I$ such that $\alpha'(a)=\beta'(a)$, then $\alpha=\beta$

Published on 19 Apr 2016 - 5:05

score 118 · Answer 4 · 2016-04-24 04:09:59

118

Views

Show that , for all $(s_{0},t_{0})\in [0,1]\times [0,a]$, the curves $s\to f(s,t_{0})$, $t\to f(s_{0},t)$ are orthogonals.

Published on 24 Apr 2016 - 4:09

score 114 · Answer 5 · 2016-04-25 00:46:43

114

Views

Question about homogeneity of the geodesic

Published on 25 Apr 2016 - 0:46

score 2.6k · Answer 6 · 2026-03-28 07:05:04

2.6k

Views

Solving constrained Euler-Lagrange equations with Lagrange Multipliers (Geodesics)

Published on 28 Mar 2026 - 7:05

score 278 · Answer 7 · 2016-04-27 10:21:36

278

Views

Two geodesics cannot form a simple region

Published on 27 Apr 2016 - 10:21

score 863 · Answer 8 · 2016-04-27 21:28:49

863

Views

How to reparametrize a geodesic such that $\nabla_V V = 0$

Published on 27 Apr 2016 - 21:28

score 515 · Answer 9 · 2016-05-03 21:32:43

515

Views

Strongly convex set is contractible

Published on 03 May 2016 - 21:32

score 304 · Answer 10 · 2016-05-09 18:06:17

304

Views

How to prove that the unit circle in the $x$-$y$ plane is a geodesic on the hyperboloid $x^2+y^2-z^2=1$?

Published on 09 May 2016 - 18:06

score 117 · Answer 11 · 2016-05-14 15:44:40

117

Views

Total Variation and geodesic Curvature

Published on 14 May 2016 - 15:44

score 1.1k · Answer 12 · 2016-05-14 22:36:06

1.1k

Views

Diffeomorphism maps geodesics to geodesics

Published on 14 May 2016 - 22:36

score 75 · Answer 13 · 2026-03-27 04:21:54

75

Views

Apply flow of $V$ to a segment of a curve, Do you get covariant derivative?

Published on 27 Mar 2026 - 4:21

score 801 · Answer 14 · 2016-05-29 14:44:15

801

Views

Solving the Euler-Lagrange equations for geodesics

Published on 29 May 2016 - 14:44

score 570 · Answer 15 · 2016-06-06 01:51:33

570

Views

Geodesic of metric space

Published on 06 Jun 2016 - 1:51

List Question

An intuitive question about the metric $d(\cdot,\cdot)$ on a complete Riemannian manifold

Show that exist a unique field $G$ on $TM$ whose paths are of the form $t\to (\gamma(t),\gamma'(t))$, where $\gamma$ is a geodesic on $M$.

Let $\alpha, \beta:I\to M$, two geodesic. If exist a number $a\in I$ such that $\alpha'(a)=\beta'(a)$, then $\alpha=\beta$

Show that , for all $(s_{0},t_{0})\in [0,1]\times [0,a]$, the curves $s\to f(s,t_{0})$, $t\to f(s_{0},t)$ are orthogonals.

Question about homogeneity of the geodesic

Solving constrained Euler-Lagrange equations with Lagrange Multipliers (Geodesics)

Two geodesics cannot form a simple region

How to reparametrize a geodesic such that $\nabla_V V = 0$

Strongly convex set is contractible

How to prove that the unit circle in the $x$-$y$ plane is a geodesic on the hyperboloid $x^2+y^2-z^2=1$?

Total Variation and geodesic Curvature

Diffeomorphism maps geodesics to geodesics

Apply flow of $V$ to a segment of a curve, Do you get covariant derivative?

Solving the Euler-Lagrange equations for geodesics

Geodesic of metric space

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