List questions from smooth-manifolds

Published on 25 Mar 2026 - 20:12

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A closed Riemannian manifold of nonpositive sectional curvature with finite $\pi_1 (M)$

Published on 25 Mar 2026 - 7:45

290

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Show that a $k$-form $\omega$ is smooth if only if it is smooth as map $\omega : M\rightarrow \Lambda ^k(M)$

Published on 26 Mar 2026 - 17:32

202

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$k$-form $\omega$ is smooth iff it is smooth as a section $\omega \colon M\rightarrow \Lambda ^k(M)$ of $\pi$

Published on 26 Mar 2026 - 16:06

61

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Looking for references: Differencial geometry a unified treatment of smooth and discrete cases

Published on 25 Mar 2026 - 3:04

42

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The rank of a map inducing a manifold

Published on 26 Mar 2026 - 14:43

597

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A special parallelization of $S^3$

Published on 26 Mar 2026 - 9:49

1.4k

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Are integral curves of a vector field $X$ such that $\nabla_X X = 0$ geodesics?

Published on 25 Mar 2026 - 18:50

104

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Well-definition of a derivation

Published on 27 Mar 2026 - 0:52

450

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Show that differential map $df : TM \to \mathbb{R}$ of a smooth map $f: M \to \mathbb{R}$ is smooth.

Published on 24 Mar 2026 - 23:48

572

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Smooth structure of a zero-dimensional manifold

Published on 26 Mar 2026 - 9:49

1k

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Projection $\pi_i : M_1 \times \cdots \times M_n \to M_i$ is a Smooth Submersion?

Published on 26 Mar 2026 - 11:18

454

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Group action map of a Lie group on a smooth manifold being submersion

Published on 25 Mar 2026 - 9:50

152

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Proof that $U(n)$ is a manifold

Published on 27 Mar 2026 - 3:57

191

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How to define orientation mapping for parametrization of a 1-manifold in a 1 dimensional space

Published on 25 Mar 2026 - 6:12

List Question

Find all parallel vector fields along a curve

A closed Riemannian manifold of nonpositive sectional curvature with finite $\pi_1 (M)$

Show that a $k$-form $\omega$ is smooth if only if it is smooth as map $\omega : M\rightarrow \Lambda ^k(M)$

$k$-form $\omega$ is smooth iff it is smooth as a section $\omega \colon M\rightarrow \Lambda ^k(M)$ of $\pi$

Looking for references: Differencial geometry a unified treatment of smooth and discrete cases

The rank of a map inducing a manifold

A special parallelization of $S^3$

Are integral curves of a vector field $X$ such that $\nabla_X X = 0$ geodesics?

Well-definition of a derivation

Show that differential map $df : TM \to \mathbb{R}$ of a smooth map $f: M \to \mathbb{R}$ is smooth.

Smooth structure of a zero-dimensional manifold

Projection $\pi_i : M_1 \times \cdots \times M_n \to M_i$ is a Smooth Submersion?

Group action map of a Lie group on a smooth manifold being submersion

Proof that $U(n)$ is a manifold

How to define orientation mapping for parametrization of a 1-manifold in a 1 dimensional space

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