Question

Show that the torsion of a connection is an element in $\Omega^2(M,TM)$

score 122 · Answer 1 · 2026-04-03 03:00:38

122

Views

Show that the torsion of a connection is an element in $\Omega^2(M,TM)$

Published on 03 Apr 2026 - 3:00

score 83 · Answer 2 · 2020-01-06 06:18:29

83

Views

How do we compute the differential of a smooth map restricted on an embedded submanifold?

Published on 06 Jan 2020 - 6:18

score 180 · Answer 3 · 2026-03-29 05:10:43

180

Views

Projectable vector fields on principal $G$ bundles

Published on 29 Mar 2026 - 5:10

score 419 · Answer 4 · 2026-03-25 12:15:26

419

Views

Is the map assigning to $x$ its tangent space smooth?

Published on 25 Mar 2026 - 12:15

score 505 · Answer 5 · 2026-03-25 17:35:44

505

Views

"A typical function is morse"

Published on 25 Mar 2026 - 17:35

score 532 · Answer 6 · 2026-04-04 01:55:34

532

Views

If the image of an injective immersion is a topological manifold, must it be an embedded smooth submanifold?

Published on 04 Apr 2026 - 1:55

score 143 · Answer 7 · 2026-03-30 14:59:28

143

Views

Why are embedded spheres removed in the connected sum but not in the handle attachment of (smooth) manifolds?

Published on 30 Mar 2026 - 14:59

score 87 · Answer 8 · 2020-01-09 12:53:44

87

Views

Dependence of smoothness of a real-valued function on a manifold

Published on 09 Jan 2020 - 12:53

score 43 · Answer 9 · 2020-01-09 23:30:08

43

Views

Tangent vector on a manifold in infinite-dimensional space $\mathbb{R}^A$, $A$ any index set (Milnor-Stasheff Lemma 1.2)

Published on 09 Jan 2020 - 23:30

score 561 · Answer 10 · 2026-03-25 12:15:04

561

Views

Components of shape operator in graph coordinates

Published on 25 Mar 2026 - 12:15

score 1.4k · Answer 11 · 2026-03-31 10:39:05

1.4k

Views

What is the meaning of "nowhere vanishing form"?!

Published on 31 Mar 2026 - 10:39

score 830 · Answer 12 · 2026-03-31 10:35:30

830

Views

Why this special method introduce a nowhere vanishing form on $\mathbb{S^1}$?

Published on 31 Mar 2026 - 10:35

score 180 · Answer 13 · 2026-03-31 10:37:13

180

Views

What is my mistake in the following proof?

Published on 31 Mar 2026 - 10:37

score 57 · Answer 14 · 2026-03-25 01:27:24

57

Views

Non-smoothness of equivalence relation on Möbius band

Published on 25 Mar 2026 - 1:27

score 231 · Answer 15 · 2026-03-25 20:35:07

231

Views

$\bar{\partial}$-exact vs $d$-exact Kähler form

Published on 25 Mar 2026 - 20:35

List Question

Show that the torsion of a connection is an element in $\Omega^2(M,TM)$

How do we compute the differential of a smooth map restricted on an embedded submanifold?

Projectable vector fields on principal $G$ bundles

Is the map assigning to $x$ its tangent space smooth?

"A typical function is morse"

If the image of an injective immersion is a topological manifold, must it be an embedded smooth submanifold?

Why are embedded spheres removed in the connected sum but not in the handle attachment of (smooth) manifolds?

Dependence of smoothness of a real-valued function on a manifold

Tangent vector on a manifold in infinite-dimensional space $\mathbb{R}^A$, $A$ any index set (Milnor-Stasheff Lemma 1.2)

Components of shape operator in graph coordinates

What is the meaning of "nowhere vanishing form"?!

Why this special method introduce a nowhere vanishing form on $\mathbb{S^1}$?

What is my mistake in the following proof?

Non-smoothness of equivalence relation on Möbius band

$\bar{\partial}$-exact vs $d$-exact Kähler form

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