List questions from differential-geometry

Published on 13 Apr 2026 - 11:17

190

Views

Standard form of the Riemannian metric in a neighborhood

Published on 16 Apr 2026 - 6:59

47

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Expressing the coordinate dependent and indepent forms of the $(0,1)$ tensor in different coordinate systems

Published on 12 Apr 2026 - 14:21

172

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One-dimensional null space for a 2-form

Published on 12 Apr 2026 - 13:57

218

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Curvature and Parametrization of the Pacman Curve

Published on 17 Apr 2026 - 6:13

51

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About the exponential map $\exp: T_pM \to M$

Published on 14 Apr 2026 - 17:53

32

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Geodesics in compact subsets of $TM$?

Published on 08 Apr 2026 - 17:42

180

Views

Prove that $f$ is Morse function if an only if $det(H)^2 + \sum_{i=1}^k (\frac {\partial f}{\partial x_i})^2>0$(2)

Published on 14 Apr 2026 - 19:37

152

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Hopf-Rinow theorem (Metric completeness implies Geodesic completeness)

Published on 15 Apr 2026 - 6:51

55

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Applicability of a $1$-form picking just one vector in the cotanget space

Published on 14 Apr 2026 - 6:27

443

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Path components of space of almost complex structures

Published on 26 Mar 2026 - 21:03

44

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can a basis for the tangent space of a manifold be found without any use of charts?

Published on 13 Apr 2026 - 20:09

55

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$U\subset \mathbb{R}^d$ open connected, $\varphi:U\to \mathbb{R}^m$ differentiable, injective, regular. Is $\varphi\left (U\right )$ a manifold?

Published on 16 Apr 2026 - 2:45

365

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Musical Isomorphisms

Published on 15 Apr 2026 - 3:48

137

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Why is the horizontal line $t\mapsto(t,y_0)$ not a geodesic in the Poincaré halfplane?

Published on 16 Apr 2026 - 23:50

List Question

Showing that a 2-form on an odd dimensional space is not degenerate

Standard form of the Riemannian metric in a neighborhood

Expressing the coordinate dependent and indepent forms of the $(0,1)$ tensor in different coordinate systems

One-dimensional null space for a 2-form

Curvature and Parametrization of the Pacman Curve

About the exponential map $\exp: T_pM \to M$

Geodesics in compact subsets of $TM$?

Prove that $f$ is Morse function if an only if $det(H)^2 + \sum_{i=1}^k (\frac {\partial f}{\partial x_i})^2>0$(2)

Hopf-Rinow theorem (Metric completeness implies Geodesic completeness)

Applicability of a $1$-form picking just one vector in the cotanget space

Path components of space of almost complex structures

can a basis for the tangent space of a manifold be found without any use of charts?

$U\subset \mathbb{R}^d$ open connected, $\varphi:U\to \mathbb{R}^m$ differentiable, injective, regular. Is $\varphi\left (U\right )$ a manifold?

Musical Isomorphisms

Why is the horizontal line $t\mapsto(t,y_0)$ not a geodesic in the Poincaré halfplane?

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