List questions from smooth-manifolds

Published on 28 Mar 2026 - 13:59

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Are the two definitions of that a map $F:A\to N$ is smooth on $A$ equivalent?

Published on 25 Mar 2026 - 11:04

104

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Almost volume preserving charts for a riemannian manifold

Published on 11 Dec 2018 - 13:50

1.3k

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Proving that the image of an injective, proper immersion is a manifold

Published on 26 Mar 2026 - 15:17

183

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Smooth bijection and tangent spaces

Published on 11 Dec 2018 - 16:34

70

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Prove that an integration is left invariant.

Published on 25 Mar 2026 - 11:10

1.1k

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Embedding a compact manifold in $\mathbb{R}^N$

Published on 25 Mar 2026 - 6:09

48

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Is $W$ a finite-dimensional vector space in Proposition 3.13?

Published on 29 Mar 2026 - 12:24

825

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Is the projection from $\mathbb R^n$ locally isometric to the flat torus?

Published on 28 Mar 2026 - 2:23

637

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integral curve starting at a zero of a vector field

Published on 25 Mar 2026 - 4:40

99

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How many unequal metrics can one define on a torus such that the projection map from $\mathbb R^n$ to the torus is a local isometry?

Published on 28 Mar 2026 - 2:24

176

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Let $M$ be a smooth manifold. Can we say that $M - M = \{ n - m : n,m \in M\}$ is also a smooth manifold?

Published on 29 Mar 2026 - 11:06

514

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If $f : M \to N$ is $C^k$, then $\Gamma(f)$ is a closed embedded submanifold of $M \times N$

Published on 25 Mar 2026 - 3:04

295

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In what dimensions are PL and Diff equivalent?

Published on 29 Mar 2026 - 11:07

81

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Perfect subgroups of $S^3$

Published on 28 Mar 2026 - 21:06

List Question

'Constant' vector field on a Lie group is smooth

Are the two definitions of that a map $F:A\to N$ is smooth on $A$ equivalent?

Almost volume preserving charts for a riemannian manifold

Proving that the image of an injective, proper immersion is a manifold

Smooth bijection and tangent spaces

Prove that an integration is left invariant.

Embedding a compact manifold in $\mathbb{R}^N$

Is $W$ a finite-dimensional vector space in Proposition 3.13?

Is the projection from $\mathbb R^n$ locally isometric to the flat torus?

integral curve starting at a zero of a vector field

How many unequal metrics can one define on a torus such that the projection map from $\mathbb R^n$ to the torus is a local isometry?

Let $M$ be a smooth manifold. Can we say that $M - M = \{ n - m : n,m \in M\}$ is also a smooth manifold?

If $f : M \to N$ is $C^k$, then $\Gamma(f)$ is a closed embedded submanifold of $M \times N$

In what dimensions are PL and Diff equivalent?

Perfect subgroups of $S^3$

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