Question

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

score 37 · Answer 1 · 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 111 · Answer 2 · 2026-03-30 23:13:31

111

Views

Given a smooth map $g: M\to R^+$, show that there is a smooth function $f:M → R^+$ such that $f(x) < g(x)$ for all $x ∈ M$.

Published on 30 Mar 2026 - 23:13

score 77 · Answer 3 · 2026-03-25 09:43:10

77

Views

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

Published on 25 Mar 2026 - 9:43

score 498 · Answer 4 · 2026-03-25 06:07:11

498

Views

For which values of $a$, is ${M_{a}=\left\{(x, y) : y^{2}=x(x-1)(x-a)\right\}}$ a sub manifold?

Published on 25 Mar 2026 - 6:07

score 62 · Answer 5 · 2026-03-31 05:41:31

62

Views

if a tangent at a point of a manifold taken as a function is zero at two points, it is zero at all points

Published on 31 Mar 2026 - 5:41

score 392 · Answer 6 · 2019-04-22 03:56:14

392

Views

Differentiable structure in $S^1$ such that the inclusion map is differentiable

Published on 22 Apr 2019 - 3:56

score 43 · Answer 7 · 2026-03-31 01:23:09

43

Views

Difficulty understanding how to construct different smooth structures on a manifold using the identity map

Published on 31 Mar 2026 - 1:23

score 1.1k · Answer 8 · 2026-03-25 07:45:44

1.1k

Views

Find $f$ such that $f^{-1}(\lbrace0\rbrace)$ is this knotted curve (M.W.Hirsh)

Published on 25 Mar 2026 - 7:45

score 335 · Answer 9 · 2026-03-30 16:02:27

335

Views

Do the two manifolds intersect at a submanifold

Published on 30 Mar 2026 - 16:02

score 54 · Answer 10 · 2026-03-30 13:40:42

54

Views

What is really being asked by "Prove that $S^1 ⊂ R^2$ is a sub manifold"?

Published on 30 Mar 2026 - 13:40

score 255 · Answer 11 · 2026-03-27 01:47:00

255

Views

Questions on coordinate representation of a map between smooth manifolds (sphere with stereographic projections)

Published on 27 Mar 2026 - 1:47

score 129 · Answer 12 · 2026-03-27 12:11:41

129

Views

Restriction of vector field to the circle

Published on 27 Mar 2026 - 12:11

score 1.2k · Answer 13 · 2026-03-27 07:48:13

1.2k

Views

Product of vector fields is not a vector field

Published on 27 Mar 2026 - 7:48

score 76 · Answer 14 · 2019-04-24 01:19:35

76

Views

Smooth regularity of Lindelof smooth manifolds modeled on smoothly regular convenient vector spaces

Published on 24 Apr 2019 - 1:19

score 659 · Answer 15 · 2026-03-29 16:01:20

659

Views

Confused about induced connection definitions, pullback bundle

Published on 29 Mar 2026 - 16:01

List Question

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

Given a smooth map $g: M\to R^+$, show that there is a smooth function $f:M → R^+$ such that $f(x) < g(x)$ for all $x ∈ M$.

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

For which values of $a$, is ${M_{a}=\left\{(x, y) : y^{2}=x(x-1)(x-a)\right\}}$ a sub manifold?

if a tangent at a point of a manifold taken as a function is zero at two points, it is zero at all points

Differentiable structure in $S^1$ such that the inclusion map is differentiable

Difficulty understanding how to construct different smooth structures on a manifold using the identity map

Find $f$ such that $f^{-1}(\lbrace0\rbrace)$ is this knotted curve (M.W.Hirsh)

Do the two manifolds intersect at a submanifold

What is really being asked by "Prove that $S^1 ⊂ R^2$ is a sub manifold"?

Questions on coordinate representation of a map between smooth manifolds (sphere with stereographic projections)

Restriction of vector field to the circle

Product of vector fields is not a vector field

Smooth regularity of Lindelof smooth manifolds modeled on smoothly regular convenient vector spaces

Confused about induced connection definitions, pullback bundle

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