List questions from riemannian-geometry

Published on 14 Apr 2026 - 18:17

893

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Hodge decomposition on Riemann surface

Published on 26 Mar 2026 - 21:35

447

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Extending Riemannian Manifold to Boundary

Published on 27 Mar 2026 - 9:57

125

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Steady Ricci solitons with negative Ricci curvature

Published on 17 Apr 2026 - 0:48

93

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Relation between inner product and wedge product

Published on 13 Apr 2026 - 4:27

134

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A differential equation and a Jacobi field

Published on 11 Apr 2026 - 5:14

87

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Gauge condition equivalent to condition that coordinate functions satisfy wave equation to first order

Published on 27 Mar 2026 - 16:22

67

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Geometric meaning of a curvature equation

Published on 12 Apr 2026 - 20:23

635

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Pullback of the metric on $\mathbb S^n$ on $\mathbb R^n$.

Published on 16 Apr 2026 - 11:16

349

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Hyperbolic isometries and finite order elements

Published on 14 Apr 2026 - 13:23

115

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Why $\nabla _{\dot \gamma (t)}Y_t=\dot x^i \frac{\mathrm d a^j(t)}{\mathrm d t}\partial _j+\dot x^i a^j\nabla _{\partial _i}\partial _j$

Published on 15 Apr 2026 - 21:31

430

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Is it always possible to always choose coordinates so that the curvature is locally zero?

Published on 14 Apr 2026 - 2:30

270

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If $\pi:\widetilde{M}\to M$ is a covering map, $M$ is complete iff $\widetilde{M}$ is complete

Published on 14 Apr 2026 - 23:10

223

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Show that geodesic equation is given by $\ddot x^k +\Gamma_{ij}^k \dot x^i\dot x^j=0$

Published on 17 Apr 2026 - 8:15

89

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Useful Formulas Analysis on Manifold

Published on 09 Apr 2026 - 5:49

List Question

Covariant derivative of a tensor field

Hodge decomposition on Riemann surface

Extending Riemannian Manifold to Boundary

Steady Ricci solitons with negative Ricci curvature

Relation between inner product and wedge product

A differential equation and a Jacobi field

Gauge condition equivalent to condition that coordinate functions satisfy wave equation to first order

Geometric meaning of a curvature equation

Pullback of the metric on $\mathbb S^n$ on $\mathbb R^n$.

Hyperbolic isometries and finite order elements

Why $\nabla _{\dot \gamma (t)}Y_t=\dot x^i \frac{\mathrm d a^j(t)}{\mathrm d t}\partial _j+\dot x^i a^j\nabla _{\partial _i}\partial _j$

Is it always possible to always choose coordinates so that the curvature is locally zero?

If $\pi:\widetilde{M}\to M$ is a covering map, $M$ is complete iff $\widetilde{M}$ is complete

Show that geodesic equation is given by $\ddot x^k +\Gamma_{ij}^k \dot x^i\dot x^j=0$

Useful Formulas Analysis on Manifold

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