Question

About the tangent cone and tangent space of an affine variety

score 948 · Answer 1 · 2019-02-15 16:34:06

948

Views

About the tangent cone and tangent space of an affine variety

Published on 15 Feb 2019 - 16:34

score 81 · Answer 2 · 2019-02-17 10:34:36

81

Views

Understanding the definition of Lie derivative

Published on 17 Feb 2019 - 10:34

score 211 · Answer 3 · 2019-03-05 17:26:37

211

Views

KIlling vectors from isometries and orbit spaces

Published on 05 Mar 2019 - 17:26

score 31 · Answer 4 · 2019-03-11 02:35:32

31

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 11 Mar 2019 - 2:35

score 593 · Answer 5 · 2019-03-13 15:46:56

593

Views

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

Published on 13 Mar 2019 - 15:46

score 310 · Answer 6 · 2019-03-21 19:20:43

310

Views

Quotient by a subring and not an ideal

Published on 21 Mar 2019 - 19:20

score 379 · Answer 7 · 2019-03-31 22:14:51

379

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 31 Mar 2019 - 22:14

score 56 · Answer 8 · 2019-04-01 22:57:03

56

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 01 Apr 2019 - 22:57

score 121 · Answer 9 · 2019-04-07 06:05:57

121

Views

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

Published on 07 Apr 2019 - 6:05

score 186 · Answer 10 · 2019-04-10 12:43:15

186

Views

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

Published on 10 Apr 2019 - 12:43

score 524 · Answer 11 · 2026-03-25 03:03:49

524

Views

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

Published on 25 Mar 2026 - 3:03

score 37 · Answer 12 · 2026-03-25 03:04:34

37

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 25 Mar 2026 - 3:04

score 76 · Answer 13 · 2019-04-21 07:24:25

76

Views

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

Published on 21 Apr 2019 - 7:24

score 61 · Answer 14 · 2019-04-22 21:23:25

61

Views

Clarification regarding the definition of a Tangent Space

Published on 22 Apr 2019 - 21:23

score 518 · Answer 15 · 2019-05-03 13:54:40

518

Views

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

Published on 03 May 2019 - 13:54

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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