List questions from riemannian-geometry

Published on 15 Apr 2026 - 10:25

638

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Sectional curvature in a paraboloid is always positive.

Published on 09 Apr 2026 - 23:43

488

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Equivalence of definitions of Killing vector field

Published on 02 Jan 2016 - 21:40

121

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Functions determine geometry ... Riemannian / metric geometry?

Published on 15 Apr 2026 - 6:40

1.1k

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Show that $\text{grad }f=\frac{f_uG-f_vF}{EG-F^2}\textbf{x}_u+\frac{f_vE-f_uF}{EG-F^2}\textbf{x}_v$

Published on 17 Apr 2026 - 2:56

136

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Is $0 = \nabla_Xg(Y, -)(Z) = \nabla_X(g(Y, Z)) - g(Y, \nabla_XZ)$ if $\nabla g= 0$?

Published on 14 Apr 2026 - 6:06

42

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$H^1_0(M)$ for non-compact $M$

Published on 13 Apr 2026 - 0:47

101

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Prove that $X = \sin \phi \,\partial_\theta + \cot \theta \cos \phi\, \partial_\phi$ is a Killing vector field

Published on 04 Apr 2026 - 7:00

269

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the distribution of Martinet

Published on 11 Apr 2026 - 5:41

283

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Distances in geodesic triangles

Published on 15 Apr 2026 - 9:45

891

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Triangulation of Torus in three different ways, but two of them are wrong.

Published on 26 Mar 2026 - 12:37

222

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Conformality of stereographic projection

Published on 10 Apr 2026 - 20:50

325

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Proof of Synge theorem without homotopy

Published on 09 Apr 2026 - 6:45

251

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Non-trivial vector field with divergence $0$ on $\mathbb{S}^{2}$.

Published on 16 Apr 2026 - 7:10

1.1k

Views

Metric tensor second derivative in terms of riemann curvature tensor NOT in a local coordinate system

Published on 13 Apr 2026 - 3:45

List Question

The tensor product of two riemannian metrics

Sectional curvature in a paraboloid is always positive.

Equivalence of definitions of Killing vector field

Functions determine geometry ... Riemannian / metric geometry?

Show that $\text{grad }f=\frac{f_uG-f_vF}{EG-F^2}\textbf{x}_u+\frac{f_vE-f_uF}{EG-F^2}\textbf{x}_v$

Is $0 = \nabla_Xg(Y, -)(Z) = \nabla_X(g(Y, Z)) - g(Y, \nabla_XZ)$ if $\nabla g= 0$?

$H^1_0(M)$ for non-compact $M$

Prove that $X = \sin \phi \,\partial_\theta + \cot \theta \cos \phi\, \partial_\phi$ is a Killing vector field

the distribution of Martinet

Distances in geodesic triangles

Triangulation of Torus in three different ways, but two of them are wrong.

Conformality of stereographic projection

Proof of Synge theorem without homotopy

Non-trivial vector field with divergence $0$ on $\mathbb{S}^{2}$.

Metric tensor second derivative in terms of riemann curvature tensor NOT in a local coordinate system

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