Question

About the tangent cone and tangent space of an affine variety

score 952 · Answer 1 · 2026-05-11 01:29:10

952

Views

About the tangent cone and tangent space of an affine variety

Published on 11 May 2026 - 1:29

score 85 · Answer 2 · 2026-05-10 14:59:54

85

Views

Understanding the definition of Lie derivative

Published on 10 May 2026 - 14:59

score 214 · Answer 3 · 2026-04-13 00:42:49

214

Views

KIlling vectors from isometries and orbit spaces

Published on 13 Apr 2026 - 0:42

score 33 · Answer 4 · 2026-05-10 15:46:38

33

Views

Consider the real-valued function $M:=\{(x,y,z)| (2 - (x^2 + y^2)^{1/2})^2 + z^2=1\}$ defined on $\mathbb{R}^3-\{(0, 0, z)\}$.

Published on 10 May 2026 - 15:46

score 596 · Answer 5 · 2026-04-14 22:08:11

596

Views

Lie bracket of canonical vectors on tangent space to a point on a manifold is zero.

Published on 14 Apr 2026 - 22:08

score 315 · Answer 6 · 2026-04-16 18:57:23

315

Views

Quotient by a subring and not an ideal

Published on 16 Apr 2026 - 18:57

score 382 · Answer 7 · 2026-04-15 00:27:20

382

Views

Show that if $f$ is a smooth function, $M$ is a manifold and $x$ is a local extremum of $f$ on $M$, then $D_f(x)(v) = 0$ in the tangent space.

Published on 15 Apr 2026 - 0:27

score 59 · Answer 8 · 2026-04-14 20:55:18

59

Views

Show that if $f$ is constant on a manifold $M$ then $\nabla f$ is orthogonal to the tangent space of each $x \in M$

Published on 14 Apr 2026 - 20:55

score 124 · Answer 9 · 2026-04-11 06:33:33

124

Views

Finding points on a surface $\{ z= f(x, y)\}$ with horizontal tangent plane

Published on 11 Apr 2026 - 6:33

score 189 · Answer 10 · 2026-04-11 16:09:50

189

Views

Are the spaces $T_pM$ and $\mathbb R^n$ homeomorphic?

Published on 11 Apr 2026 - 16:09

score 527 · Answer 11 · 2026-05-11 00:32:50

527

Views

Determining the linear independence of tangent vectors at a point on the manifold

Published on 11 May 2026 - 0:32

score 39 · Answer 12 · 2026-04-18 04:55:07

39

Views

For any k-dim. subspace $ L$ of $T_p M$, can we find a sub manifold, say $R$, of $M$ containing $p$ s.t $T_p R = L$

Published on 18 Apr 2026 - 4:55

score 79 · Answer 13 · 2026-04-15 10:34:41

79

Views

Proving the well-definedness of $df$: How to place the limit inside the argument of $\psi \circ f \circ \phi^{-1}$?

Published on 15 Apr 2026 - 10:34

score 64 · Answer 14 · 2026-04-11 07:45:33

64

Views

Clarification regarding the definition of a Tangent Space

Published on 11 Apr 2026 - 7:45

score 521 · Answer 15 · 2026-04-09 08:59:55

521

Views

Realizing every rotation of a tangent space on a sphere as a parallel transport

Published on 09 Apr 2026 - 8:59

List Question

About the tangent cone and tangent space of an affine variety

Understanding the definition of Lie derivative

KIlling vectors from isometries and orbit spaces

Consider the real-valued function $M:=\{(x,y,z)| (2 - (x^2 + y^2)^{1/2})^2 + z^2=1\}$ defined on $\mathbb{R}^3-\{(0, 0, z)\}$.

Lie bracket of canonical vectors on tangent space to a point on a manifold is zero.

Quotient by a subring and not an ideal

Show that if $f$ is a smooth function, $M$ is a manifold and $x$ is a local extremum of $f$ on $M$, then $D_f(x)(v) = 0$ in the tangent space.

Show that if $f$ is constant on a manifold $M$ then $\nabla f$ is orthogonal to the tangent space of each $x \in M$

Finding points on a surface $\{ z= f(x, y)\}$ with horizontal tangent plane

Are the spaces $T_pM$ and $\mathbb R^n$ homeomorphic?

Determining the linear independence of tangent vectors at a point on the manifold

For any k-dim. subspace $ L$ of $T_p M$, can we find a sub manifold, say $R$, of $M$ containing $p$ s.t $T_p R = L$

Proving the well-definedness of $df$: How to place the limit inside the argument of $\psi \circ f \circ \phi^{-1}$?

Clarification regarding the definition of a Tangent Space

Realizing every rotation of a tangent space on a sphere as a parallel transport

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