Question

How to show that This Linear map satisfies $T(f)=f'(0)$

score 49 · Answer 1 · 2021-11-08 12:00:58

49

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How to show that This Linear map satisfies $T(f)=f'(0)$

Published on 08 Nov 2021 - 12:00

score 74 · Answer 2 · 2021-11-08 12:33:08

74

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Proving $X(f)=X(g)$, where $X\in T_p(M)$ and $f(x) =g(x)$ for all $x\in U\subseteq M $

Published on 08 Nov 2021 - 12:33

score 57 · Answer 3 · 2021-11-09 15:25:09

57

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Do vector fields on manifold have to be defined using derivatives?

Published on 09 Nov 2021 - 15:25

score 143 · Answer 4 · 2021-11-10 05:39:46

143

Views

Why do we need a scalar function $f$ to define tangent vectors on a manifold

Published on 10 Nov 2021 - 5:39

score 64 · Answer 5 · 2021-11-10 06:25:34

64

Views

What is and what is an example of the function that Partial Derivative basis vectors act on in differential geometry?

Published on 10 Nov 2021 - 6:25

score 228 · Answer 6 · 2021-11-12 08:23:47

228

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Show that f is constant on Connected submanifold S of M

Published on 12 Nov 2021 - 8:23

score 303 · Answer 7 · 2026-03-27 14:58:49

303

Views

Definition of a tangent vector as a differential operator via Tangent Map?

Published on 27 Mar 2026 - 14:58

score 40 · Answer 8 · 2026-03-25 22:04:25

40

Views

Transversality just on a single point but not in any neighborhood

Published on 25 Mar 2026 - 22:04

score 30 · Answer 9 · 2021-11-20 22:45:12

30

Views

Is this justification of derivative operators as tangent vectors correct?

Published on 20 Nov 2021 - 22:45

score 148 · Answer 10 · 2021-11-22 13:43:00

148

Views

The dimension of a tangent space of a smooth $k$-dimensional manifold is actually $k$

Published on 22 Nov 2021 - 13:43

score 176 · Answer 11 · 2021-11-22 17:17:02

176

Views

The tangent space is well-defined

Published on 22 Nov 2021 - 17:17

score 79 · Answer 12 · 2021-12-07 18:36:04

79

Views

How do I make sense of the following definitions of tangent vectors?

Published on 07 Dec 2021 - 18:36

score 87 · Answer 13 · 2021-12-10 13:29:59

87

Views

Theorem 8.5 (The chain rule) from "An introduction to manifolds" by Tu - How should I understand the notation $(...)f$ where $f$ is a smooth function?

Published on 10 Dec 2021 - 13:29

score 319 · Answer 14 · 2021-12-14 01:28:29

319

Views

Coordinate-free definition of tangent space of differentiable manifold

Published on 14 Dec 2021 - 1:28

score 212 · Answer 15 · 2021-12-22 14:52:48

212

Views

Preimage of a regular value : proving that the tangent plane is given by the kernel of the differential

Published on 22 Dec 2021 - 14:52

List Question

How to show that This Linear map satisfies $T(f)=f'(0)$

Proving $X(f)=X(g)$, where $X\in T_p(M)$ and $f(x) =g(x)$ for all $x\in U\subseteq M $

Do vector fields on manifold have to be defined using derivatives?

Why do we need a scalar function $f$ to define tangent vectors on a manifold

What is and what is an example of the function that Partial Derivative basis vectors act on in differential geometry?

Show that f is constant on Connected submanifold S of M

Definition of a tangent vector as a differential operator via Tangent Map?

Transversality just on a single point but not in any neighborhood

Is this justification of derivative operators as tangent vectors correct?

The dimension of a tangent space of a smooth $k$-dimensional manifold is actually $k$

The tangent space is well-defined

How do I make sense of the following definitions of tangent vectors?

Theorem 8.5 (The chain rule) from "An introduction to manifolds" by Tu - How should I understand the notation $(...)f$ where $f$ is a smooth function?

Coordinate-free definition of tangent space of differentiable manifold

Preimage of a regular value : proving that the tangent plane is given by the kernel of the differential

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