Question

Vector fields (on a manifold) and terminology

score 587 · Answer 1 · 2026-04-07 20:57:51

587

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Vector fields (on a manifold) and terminology

Published on 07 Apr 2026 - 20:57

score 505 · Answer 2 · 2026-04-06 00:16:19

505

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Do I have the right idea about affine connections?

Published on 06 Apr 2026 - 0:16

score 1.1k · Answer 3 · 2026-03-29 07:40:24

1.1k

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How to prove that there are only two kinds of 1-dim manifolds without boundary

Published on 29 Mar 2026 - 7:40

score 84 · Answer 4 · 2026-04-06 12:41:13

84

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Construct a diffeomorphism $\psi: B_1 \to \epsilon\text{-neighborhood of } K$, where $K$ is a subset of a smooth manifold.

Published on 06 Apr 2026 - 12:41

score 1.1k · Answer 5 · 2016-07-23 06:06:21

1.1k

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addition of two differential forms with different degrees

Published on 23 Jul 2016 - 6:06

score 87 · Answer 6 · 2026-04-06 14:18:43

87

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Construct smooth mapping $f: B^{n + 1} \to S^n$ with two singularities at which $f$ has degree $+/- 1$.

Published on 06 Apr 2026 - 14:18

score 275 · Answer 7 · 2026-04-06 14:19:51

275

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Definition of manifold which are subset of euclidean space

Published on 06 Apr 2026 - 14:19

score 544 · Answer 8 · 2026-03-30 03:23:24

544

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Poincaré–Bendixson theorem on the torus

Published on 30 Mar 2026 - 3:23

score 1.1k · Answer 9 · 2026-03-25 15:39:19

1.1k

Views

Viewing complex projective space as a Grassmannian manifold

Published on 25 Mar 2026 - 15:39

score 61 · Answer 10 · 2026-03-26 06:32:39

61

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If $M^n$ is a submanifold of $\mathbb{R}^{n+k}$ such there are L.I. vector fields $v_1,\ldots,v_k$ such that $v_i \perp T_pM$ then $M$ is orientable

Published on 26 Mar 2026 - 6:32

score 1.2k · Answer 11 · 2026-03-26 01:07:55

1.2k

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Jacobian determinant of a function $f$ if it has a differentiable inverse.

Published on 26 Mar 2026 - 1:07

score 164 · Answer 12 · 2026-03-30 22:37:10

164

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Let $X_i, Y_i$ be vector fields on the manifolds M and N. $X_i\oplus Y_j$ on $M\times N$. $[X_1\oplus Y_1,X_2\oplus Y_2]=[X_1,Y_1]\oplus [X_2,Y_2]$

Published on 30 Mar 2026 - 22:37

score 147 · Answer 13 · 2026-04-05 21:29:33

147

Views

rho invariant of manifold

Published on 05 Apr 2026 - 21:29

score 115 · Answer 14 · 2026-03-31 05:26:09

115

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$f:M\to N$ smooth manifold map. $F(x)=(x,f(x))\in M\times N$. For each $X\in \mathfrak{X}(M)$ there's a F-related $Y\in \mathfrak{X}(M\times N)$.

Published on 31 Mar 2026 - 5:26

score 1k · Answer 15 · 2026-04-06 01:59:30

1k

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First and second fundamental form with rotational surfaces (check)

Published on 06 Apr 2026 - 1:59

List Question

Vector fields (on a manifold) and terminology

Do I have the right idea about affine connections?

How to prove that there are only two kinds of 1-dim manifolds without boundary

Construct a diffeomorphism $\psi: B_1 \to \epsilon\text{-neighborhood of } K$, where $K$ is a subset of a smooth manifold.

addition of two differential forms with different degrees

Construct smooth mapping $f: B^{n + 1} \to S^n$ with two singularities at which $f$ has degree $+/- 1$.

Definition of manifold which are subset of euclidean space

Poincaré–Bendixson theorem on the torus

Viewing complex projective space as a Grassmannian manifold

If $M^n$ is a submanifold of $\mathbb{R}^{n+k}$ such there are L.I. vector fields $v_1,\ldots,v_k$ such that $v_i \perp T_pM$ then $M$ is orientable

Jacobian determinant of a function $f$ if it has a differentiable inverse.

Let $X_i, Y_i$ be vector fields on the manifolds M and N. $X_i\oplus Y_j$ on $M\times N$. $[X_1\oplus Y_1,X_2\oplus Y_2]=[X_1,Y_1]\oplus [X_2,Y_2]$

rho invariant of manifold

$f:M\to N$ smooth manifold map. $F(x)=(x,f(x))\in M\times N$. For each $X\in \mathfrak{X}(M)$ there's a F-related $Y\in \mathfrak{X}(M\times N)$.

First and second fundamental form with rotational surfaces (check)

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