Question

Does the Riemannian connection commute with $(1, 1)$ tensors in the first slot?

score 70 · Answer 1 · 2023-10-29 00:35:58

70

Views

Does the Riemannian connection commute with $(1, 1)$ tensors in the first slot?

Published on 29 Oct 2023 - 0:35

score 82 · Answer 2 · 2023-10-29 06:23:55

82

Views

Showing that $\int (\partial_i f) h^j g^{ij} dV = 0$

Published on 29 Oct 2023 - 6:23

score 83 · Answer 3 · 2026-04-09 16:07:13

83

Views

Local expression of the dual of Levi-Civita connection

Published on 09 Apr 2026 - 16:07

score 204 · Answer 4 · 2026-03-25 01:38:28

204

Views

Second fundamental form of a general immersion $F:M^n\to(N^{n+1},\bar{g})$

Published on 25 Mar 2026 - 1:38

score 38 · Answer 5 · 2023-10-30 09:15:40

38

Views

Why $\alpha_M(x)=\frac{d}{dt}|_{t=0}x\cdot \exp(t\alpha)$ defines an infinitesimal action?

Published on 30 Oct 2023 - 9:15

score 113 · Answer 6 · 2023-10-31 05:48:32

Given a manifold $(M,g)$, and a $f_\alpha(x):=\exp _p(\alpha x)$, why $h_\alpha:=\alpha^{-2} f_\alpha^* g \rightarrow$ the Euclidean metric.

score 90 · Answer 7 · 2026-04-12 14:19:56

90

Views

Expected Riemannian Metric of a Random Generator Function

Published on 12 Apr 2026 - 14:19

score 59 · Answer 8 · 2026-04-11 22:23:25

59

Views

Embedding/immersion of $\mathbb RP^2$ into Euclidean space so lines are geodesics?

Published on 11 Apr 2026 - 22:23

score 48 · Answer 9 · 2026-04-12 09:06:39

48

Views

Is it true that a coercive Riemannian metric implies geodesic completeness?

Published on 12 Apr 2026 - 9:06

score 97 · Answer 10 · 2023-11-01 23:38:23

97

Views

Proof of $\frac{\partial}{\partial t}g_{ij}=2\lambda h_{ij}$ of geometric flow

Published on 01 Nov 2023 - 23:38

score 35 · Answer 11 · 2026-03-26 22:13:37

35

Views

A guess about first eigenfunction and scalar curvature on Riemannian 2-sphere

Published on 26 Mar 2026 - 22:13

score 48 · Answer 12 · 2026-03-29 15:59:57

48

Views

Least energy harmonic map onto $\mathbb S^2$

Published on 29 Mar 2026 - 15:59

score 45 · Answer 13 · 2026-04-12 11:11:40

45

Views

Completion of the tangent space of a Riemannian manifold

Published on 12 Apr 2026 - 11:11

score 87 · Answer 14 · 2026-04-12 15:18:49

87

Views

Just checking: Hessian of the distance function on the constant curvature spaces are not of full rank?

Published on 12 Apr 2026 - 15:18

score 78 · Answer 15 · 2026-03-29 15:02:31

78

Views

Requirement of Hessian comparison theorem to prove that the squared distance function is strictly geodesically convex.

Published on 29 Mar 2026 - 15:02

List Question

Does the Riemannian connection commute with $(1, 1)$ tensors in the first slot?

Showing that $\int (\partial_i f) h^j g^{ij} dV = 0$

Local expression of the dual of Levi-Civita connection

Second fundamental form of a general immersion $F:M^n\to(N^{n+1},\bar{g})$

Why $\alpha_M(x)=\frac{d}{dt}|_{t=0}x\cdot \exp(t\alpha)$ defines an infinitesimal action?

Given a manifold $(M,g)$, and a $f_\alpha(x):=\exp _p(\alpha x)$, why $h_\alpha:=\alpha^{-2} f_\alpha^* g \rightarrow$ the Euclidean metric.

Expected Riemannian Metric of a Random Generator Function

Embedding/immersion of $\mathbb RP^2$ into Euclidean space so lines are geodesics?

Is it true that a coercive Riemannian metric implies geodesic completeness?

Proof of $\frac{\partial}{\partial t}g_{ij}=2\lambda h_{ij}$ of geometric flow

A guess about first eigenfunction and scalar curvature on Riemannian 2-sphere

Least energy harmonic map onto $\mathbb S^2$

Completion of the tangent space of a Riemannian manifold

Just checking: Hessian of the distance function on the constant curvature spaces are not of full rank?

Requirement of Hessian comparison theorem to prove that the squared distance function is strictly geodesically convex.

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