Question

Why is $\{p\}\times W$ is a subspace of $T_pS$, and equal to it (S an affine subspace of $\mathbb{R}^n$)?

score 67 · Answer 1 · 2021-12-22 19:13:59

67

Views

Why is $\{p\}\times W$ is a subspace of $T_pS$, and equal to it (S an affine subspace of $\mathbb{R}^n$)?

Published on 22 Dec 2021 - 19:13

score 93 · Answer 2 · 2022-01-02 10:43:54

93

Views

Change of basis in tangent space of $C\equiv x^2+y^2=z^2, \, z>0$

Published on 02 Jan 2022 - 10:43

score 40 · Answer 3 · 2022-01-04 13:49:42

40

Views

Tangent space to a level curve

Published on 04 Jan 2022 - 13:49

score 91 · Answer 4 · 2022-01-06 12:49:39

91

Views

Tangent vectors of smooth manifolds as "modified" derivations?

Published on 06 Jan 2022 - 12:49

score 123 · Answer 5 · 2022-01-11 13:16:39

123

Views

Tangential planes on a surface at the points of intersection with the sphere

Published on 11 Jan 2022 - 13:16

score 53 · Answer 6 · 2022-01-13 11:08:29

53

Views

Showing a linear map is a derivation at a point iff it vanishes on the rank 0 map

Published on 13 Jan 2022 - 11:08

score 61 · Answer 7 · 2022-01-14 01:06:19

61

Views

Do equivalence classes of mutually tangential curves depend on choices of charts from inequivalent atlases?

Published on 14 Jan 2022 - 1:06

score 38 · Answer 8 · 2022-01-16 15:09:17

38

Views

Existence of specific curves necessary to construct $T_p(M)$

Published on 16 Jan 2022 - 15:09

score 30 · Answer 9 · 2022-01-18 21:55:15

30

Views

How to interpret the tangent vectors in easy situation?

Published on 18 Jan 2022 - 21:55

score 124 · Answer 10 · 2022-01-19 17:01:54

124

Views

Integral curve definition in terms of the tangent vector: why $D \varphi_{t} (d/dt) = X_{\varphi(t)}$?

Published on 19 Jan 2022 - 17:01

score 60 · Answer 11 · 2022-01-20 12:31:59

60

Views

Tangent space of $G/H$ at the identity

Published on 20 Jan 2022 - 12:31

score 169 · Answer 12 · 2022-01-22 15:33:33

169

Views

The derivative of a smooth map between smooth submanifolds of Euclidean spaces: Is it a best linear approximation?

Published on 22 Jan 2022 - 15:33

score 42 · Answer 13 · 2022-01-23 14:04:07

42

Views

When defining tangent spaces, given $\gamma:(-1,1)\to M$ and $\varphi:U\to\mathbb R^n,U\subseteq M$, why is $\varphi\circ\gamma:(-1,1)\to\mathbb R^n$?

Published on 23 Jan 2022 - 14:04

score 208 · Answer 14 · 2022-01-25 17:11:23

208

Views

Tangent space of $G \times_H M$

Published on 25 Jan 2022 - 17:11

score 133 · Answer 15 · 2022-01-26 11:11:58

133

Views

What is the derivative of the inclusion map $\iota: M \rightarrow G \times_H M$

Published on 26 Jan 2022 - 11:11

List Question

Why is $\{p\}\times W$ is a subspace of $T_pS$, and equal to it (S an affine subspace of $\mathbb{R}^n$)?

Change of basis in tangent space of $C\equiv x^2+y^2=z^2, \, z>0$

Tangent space to a level curve

Tangent vectors of smooth manifolds as "modified" derivations?

Tangential planes on a surface at the points of intersection with the sphere

Showing a linear map is a derivation at a point iff it vanishes on the rank 0 map

Do equivalence classes of mutually tangential curves depend on choices of charts from inequivalent atlases?

Existence of specific curves necessary to construct $T_p(M)$

How to interpret the tangent vectors in easy situation?

Integral curve definition in terms of the tangent vector: why $D \varphi_{t} (d/dt) = X_{\varphi(t)}$?

Tangent space of $G/H$ at the identity

The derivative of a smooth map between smooth submanifolds of Euclidean spaces: Is it a best linear approximation?

When defining tangent spaces, given $\gamma:(-1,1)\to M$ and $\varphi:U\to\mathbb R^n,U\subseteq M$, why is $\varphi\circ\gamma:(-1,1)\to\mathbb R^n$?

Tangent space of $G \times_H M$

What is the derivative of the inclusion map $\iota: M \rightarrow G \times_H M$

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