Question

Riemannian Manifold for the Partial Doubly Stochastic Matrices

score 167 · Answer 1 · 2026-03-25 10:53:00

167

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Riemannian Manifold for the Partial Doubly Stochastic Matrices

Published on 25 Mar 2026 - 10:53

score 143 · Answer 2 · 2019-03-06 05:32:35

143

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Show that $f(v)=f(0)+\langle df(0),v\rangle_{x}+\frac{1}{2}\langle d^{2}f(0)v,v\rangle_{x}+o(\|v\|^{2})$

Published on 06 Mar 2019 - 5:32

score 136 · Answer 3 · 2026-03-26 01:29:01

136

Views

Integrate a top form over a surface without partition of unity

Published on 26 Mar 2026 - 1:29

score 608 · Answer 4 · 2019-03-06 15:54:10

608

Views

Laplacian is the trace of Hessian in local coordinates

Published on 06 Mar 2019 - 15:54

score 1.4k · Answer 5 · 2026-03-26 07:33:26

1.4k

Views

Integration by parts for tensor fields on Riemannian manifold

Published on 26 Mar 2026 - 7:33

score 680 · Answer 6 · 2019-03-08 20:07:57

680

Views

Taylor expansion of $g^{-1/2}$ where $g$ is riemannian metric in normal coordinates

Published on 08 Mar 2019 - 20:07

score 268 · Answer 7 · 2026-03-25 06:48:48

268

Views

geodesic balls in Riemannian manifolds with bounded geometry

Published on 25 Mar 2026 - 6:48

score 149 · Answer 8 · 2026-03-25 03:03:57

149

Views

The differential $df:T(M)\rightarrow\mathbb{R}$ and the differential map $df:T(M)\rightarrow T(\mathbb{R^1})$ differ by a canonical isomorphism.

Published on 25 Mar 2026 - 3:03

score 602 · Answer 9 · 2026-03-25 14:22:52

602

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How does one prove that $\text{Isom}(\mathbb{S}^2 \times \mathbb{R}) = \text{Isom}(\mathbb{S}^2) \times \text{Isom}(\mathbb{R})$?

Published on 25 Mar 2026 - 14:22

score 63 · Answer 10 · 2019-03-11 21:21:03

63

Views

Reference request - Measure of sphere in Riemannian manifold

Published on 11 Mar 2019 - 21:21

score 108 · Answer 11 · 2019-03-12 17:44:01

What's wrong with this proof that $\text{Isom}(\mathbb{S}^2 \times \mathbb{R}) \cong \text{Isom}(\mathbb{S}^2) \times \text{Isom}(\mathbb{R})$?

score 177 · Answer 12 · 2026-03-24 22:01:58

177

Views

Does the Volume Ratio in a Complete Riemannian Manifold always tend to the Volume of the Euclidean Unit Ball?

Published on 24 Mar 2026 - 22:01

score 455 · Answer 13 · 2019-03-13 09:12:03

455

Views

Several questions about bilinear forms on Banach spaces

Published on 13 Mar 2019 - 9:12

score 189 · Answer 14 · 2026-03-25 10:56:09

189

Views

Size of $\epsilon$-net on a $2$-dimensional compact manifold

Published on 25 Mar 2026 - 10:56

score 149 · Answer 15 · 2026-03-25 21:16:56

149

Views

What kind of properties characterise "constant curvature" for a general geometry?

Published on 25 Mar 2026 - 21:16

List Question

Riemannian Manifold for the Partial Doubly Stochastic Matrices

Show that $f(v)=f(0)+\langle df(0),v\rangle_{x}+\frac{1}{2}\langle d^{2}f(0)v,v\rangle_{x}+o(\|v\|^{2})$

Integrate a top form over a surface without partition of unity

Laplacian is the trace of Hessian in local coordinates

Integration by parts for tensor fields on Riemannian manifold

Taylor expansion of $g^{-1/2}$ where $g$ is riemannian metric in normal coordinates

geodesic balls in Riemannian manifolds with bounded geometry

The differential $df:T(M)\rightarrow\mathbb{R}$ and the differential map $df:T(M)\rightarrow T(\mathbb{R^1})$ differ by a canonical isomorphism.

How does one prove that $\text{Isom}(\mathbb{S}^2 \times \mathbb{R}) = \text{Isom}(\mathbb{S}^2) \times \text{Isom}(\mathbb{R})$?

Reference request - Measure of sphere in Riemannian manifold

What's wrong with this proof that $\text{Isom}(\mathbb{S}^2 \times \mathbb{R}) \cong \text{Isom}(\mathbb{S}^2) \times \text{Isom}(\mathbb{R})$?

Does the Volume Ratio in a Complete Riemannian Manifold always tend to the Volume of the Euclidean Unit Ball?

Several questions about bilinear forms on Banach spaces

Size of $\epsilon$-net on a $2$-dimensional compact manifold

What kind of properties characterise "constant curvature" for a general geometry?

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