Question

Existence of closed "globally length minimising" geodesics on compact Riemannian manifolds

score 80 · Answer 1 · 2022-09-14 03:23:25

80

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Existence of closed "globally length minimising" geodesics on compact Riemannian manifolds

Published on 14 Sep 2022 - 3:23

score 106 · Answer 2 · 2026-03-30 00:21:10

106

Views

Prove that the geodesic between two points A and B on a spherical surface is found on the curve formed by the intersection with the plane

Published on 30 Mar 2026 - 0:21

score 75 · Answer 3 · 2022-09-20 14:10:13

75

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Smooth representatives of two free homotopy classes of loops on a surface that intersect transversally

Published on 20 Sep 2022 - 14:10

score 88 · Answer 4 · 2022-09-22 14:45:58

88

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How can I show that this curve is a great circle on the unit sphere?

Published on 22 Sep 2022 - 14:45

score 123 · Answer 5 · 2022-09-24 07:31:08

123

Views

If two points can be joined by a causal curve that is not a null geodesic, can they be joined by a timelike curve?

Published on 24 Sep 2022 - 7:31

score 34 · Answer 6 · 2022-09-24 10:27:43

34

Views

Showing bound $\|\nabla_t \dot{\tilde{x}}_Y(h, 0)\| \le L \|Y\|_{2, \infty}$ for smooth homotopies of geodesics

Published on 24 Sep 2022 - 10:27

score 56 · Answer 7 · 2026-03-25 15:57:16

56

Views

calculate angle between two points in horizontal plane

Published on 25 Mar 2026 - 15:57

score 125 · Answer 8 · 2026-03-27 07:36:31

125

Views

Geodesic distance from inner product in an embedding space

Published on 27 Mar 2026 - 7:36

score 222 · Answer 9 · 2022-10-01 11:10:19

222

Views

Distance between antipodal points in a geodesic ball

Published on 01 Oct 2022 - 11:10

score 242 · Answer 10 · 2022-10-06 16:35:07

242

Views

Do geodesics locally follow the gradient of the distance function?

Published on 06 Oct 2022 - 16:35

score 637 · Answer 11 · 2026-03-26 14:29:02

637

Views

How does Earth’s curvature affect flight times?

Published on 26 Mar 2026 - 14:29

score 88 · Answer 12 · 2022-10-19 17:20:52

88

Views

Is the distance function convex over geodesically convex sets?

Published on 19 Oct 2022 - 17:20

score 46 · Answer 13 · 2022-10-20 00:37:54

46

Views

Is a subset of a sphere that is itself contained within a hemisphere totally convex?

Published on 20 Oct 2022 - 0:37

score 44 · Answer 14 · 2026-03-26 16:11:29

44

Views

Can someone check if this “proof” is correct?

Published on 26 Mar 2026 - 16:11

score 101 · Answer 15 · 2022-10-31 21:32:50

101

Views

Proof of Theorem 1.4.1 in Ratcliffe book Foundations of Hyperbolic Manifolds

Published on 31 Oct 2022 - 21:32

List Question

Existence of closed "globally length minimising" geodesics on compact Riemannian manifolds

Prove that the geodesic between two points A and B on a spherical surface is found on the curve formed by the intersection with the plane

Smooth representatives of two free homotopy classes of loops on a surface that intersect transversally

How can I show that this curve is a great circle on the unit sphere?

If two points can be joined by a causal curve that is not a null geodesic, can they be joined by a timelike curve?

Showing bound $\|\nabla_t \dot{\tilde{x}}_Y(h, 0)\| \le L \|Y\|_{2, \infty}$ for smooth homotopies of geodesics

calculate angle between two points in horizontal plane

Geodesic distance from inner product in an embedding space

Distance between antipodal points in a geodesic ball

Do geodesics locally follow the gradient of the distance function?

How does Earth’s curvature affect flight times?

Is the distance function convex over geodesically convex sets?

Is a subset of a sphere that is itself contained within a hemisphere totally convex?

Can someone check if this “proof” is correct?

Proof of Theorem 1.4.1 in Ratcliffe book Foundations of Hyperbolic Manifolds

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