Question

A smooth vector field of a differentiable manifold represented by $\frac{\partial}{\partial x_1}$ under some coordinate chart

score 85 · Answer 1 · 2026-04-02 01:24:34

85

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A smooth vector field of a differentiable manifold represented by $\frac{\partial}{\partial x_1}$ under some coordinate chart

Published on 02 Apr 2026 - 1:24

score 100 · Answer 2 · 2023-02-19 16:30:31

100

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Why are open sets of Euclidean space obviously manifolds?

Published on 19 Feb 2023 - 16:30

score 29 · Answer 3 · 2026-03-29 18:53:36

29

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$P := \{x ∈\mathbb{R}^3 : x_3 = x_1^2 + x_2^2 < 4\}$ . Sketch $P$ and calculate its surface area.

Published on 29 Mar 2026 - 18:53

score 98 · Answer 4 · 2026-03-25 15:42:25

98

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What is the definition of sheaf of meromorphic differential form on a complex manifold？

Published on 25 Mar 2026 - 15:42

score 61 · Answer 5 · 2026-03-26 02:55:36

61

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On the definition of the second-order derivative of a Morse function

Published on 26 Mar 2026 - 2:55

score 115 · Answer 6 · 2026-04-09 07:22:48

115

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Why are tangent vectors in statistical manifolds $\boldsymbol e_i\approx \partial_i \log p(x,\boldsymbol\xi)$?

Published on 09 Apr 2026 - 7:22

score 165 · Answer 7 · 2026-03-25 08:07:41

165

Views

$\mathbb{C}P^2$ is not diffeomorphic to $\overline{\mathbb{C}P^2}$

Published on 25 Mar 2026 - 8:07

score 89 · Answer 8 · 2026-03-25 15:39:18

89

Views

Equivalent definitions of 1-forms

Published on 25 Mar 2026 - 15:39

score 108 · Answer 9 · 2023-02-24 20:40:35

108

Views

Must a topological space with the following property be a manifold?

Published on 24 Feb 2023 - 20:40

score 55 · Answer 10 · 2026-04-10 18:13:15

55

Views

A question about making topological spaces into smooth manifolds

Published on 10 Apr 2026 - 18:13

score 53 · Answer 11 · 2026-04-08 09:27:59

53

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Understanding of Partition of Unity

Published on 08 Apr 2026 - 9:27

score 36 · Answer 12 · 2023-02-26 12:13:53

36

Views

Calculate $S_2(\varphi(U))$

Published on 26 Feb 2023 - 12:13

score 93 · Answer 13 · 2026-03-31 10:04:57

93

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Restriction of a vector bundle

Published on 31 Mar 2026 - 10:04

score 52 · Answer 14 · 2026-03-29 18:37:25

52

Views

Calculate $\int_M x_1x_3dS_2$ with $M:=\{ x\in \mathbb{R}^3 x_1^2+x_2^2+x_3^2=4, x_1 \leq 0 x_2\geq 0 x_3 \geq 0 \}$

Published on 29 Mar 2026 - 18:37

score 66 · Answer 15 · 2026-04-11 22:10:08

66

Views

Derive a formula for a curve on a lie group

Published on 11 Apr 2026 - 22:10

List Question

A smooth vector field of a differentiable manifold represented by $\frac{\partial}{\partial x_1}$ under some coordinate chart

Why are open sets of Euclidean space obviously manifolds?

$P := \{x ∈\mathbb{R}^3 : x_3 = x_1^2 + x_2^2 < 4\}$ . Sketch $P$ and calculate its surface area.

What is the definition of sheaf of meromorphic differential form on a complex manifold？

On the definition of the second-order derivative of a Morse function

Why are tangent vectors in statistical manifolds $\boldsymbol e_i\approx \partial_i \log p(x,\boldsymbol\xi)$?

$\mathbb{C}P^2$ is not diffeomorphic to $\overline{\mathbb{C}P^2}$

Equivalent definitions of 1-forms

Must a topological space with the following property be a manifold?

A question about making topological spaces into smooth manifolds

Understanding of Partition of Unity

Calculate $S_2(\varphi(U))$

Restriction of a vector bundle

Calculate $\int_M x_1x_3dS_2$ with $M:=\{ x\in \mathbb{R}^3 x_1^2+x_2^2+x_3^2=4, x_1 \leq 0 x_2\geq 0 x_3 \geq 0 \}$

Derive a formula for a curve on a lie group

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