Question

Coordinate change of hypersurface differential form

score 35 · Answer 1 · 2023-12-18 20:13:37

35

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Coordinate change of hypersurface differential form

Published on 18 Dec 2023 - 20:13

score 209 · Answer 2 · 2023-12-19 17:50:18

209

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Coordinate free covariant derivative of tensor densities

Published on 19 Dec 2023 - 17:50

score 92 · Answer 3 · 2026-04-01 06:29:05

92

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Comparing the definition for the pullback of generic vector bundles and the one for differential forms

Published on 01 Apr 2026 - 6:29

score 101 · Answer 4 · 2026-03-26 17:47:30

101

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Exercise 5.22 in the book Geometrical Methods of Mathematical Physics (by Bernard Schutz)

Published on 26 Mar 2026 - 17:47

score 36 · Answer 5 · 2026-04-03 06:05:54

36

Views

Show that a frame field is (not) holonomic - only possible by going to the coframe?

Published on 03 Apr 2026 - 6:05

score 60 · Answer 6 · 2026-03-27 06:17:01

60

Views

On the conclusion of the (compact) de Rham cohomology of $\mathbb{R}$

Published on 27 Mar 2026 - 6:17

score 39 · Answer 7 · 2026-03-25 14:19:20

39

Views

Lefschetz operator on bundle-valued forms

Published on 25 Mar 2026 - 14:19

score 116 · Answer 8 · 2026-03-30 01:16:55

116

Views

What exactly does "outward normal vector" means when talking about an orientation?

Published on 30 Mar 2026 - 1:16

score 50 · Answer 9 · 2026-03-30 05:13:55

50

Views

Riemann Roch Canonical Divisor - show the divisor of a differential form does not depend on choice of local coordinates

Published on 30 Mar 2026 - 5:13

score 88 · Answer 10 · 2026-03-27 02:34:33

88

Views

Deligne complex and sheaf of chain complex

Published on 27 Mar 2026 - 2:34

score 97 · Answer 11 · 2024-01-03 18:17:36

97

Views

Relation between trilinear forms, Jacobi identity and closed $2$-forms

Published on 03 Jan 2024 - 18:17

score 81 · Answer 12 · 2026-03-28 06:15:50

81

Views

Let $\{e^1,...,e^m\}$ standard basis of $(\Bbb R^m)^*$ , $(U,\varphi)$ a chart. Why is $d(x^i\circ \varphi^{-1})_{\varphi(p)}=d(e^i)_{\phi(p)}=e^i$?

Published on 28 Mar 2026 - 6:15

score 120 · Answer 13 · 2024-01-04 15:33:41

120

Views

Decomposition of 1-forms in simply connected open subset of Euclidean space

Published on 04 Jan 2024 - 15:33

score 131 · Answer 14 · 2024-01-04 21:55:37

131

Views

Why aren't integrals invariant over coordinate transformations?

Published on 04 Jan 2024 - 21:55

score 58 · Answer 15 · 2026-03-26 17:53:36

58

Views

Computing $ι^∗(dy^j)_p( \frac{\partial}{\partial x^l}_p)$ and $ι^∗(dz^k)_p( \frac{\partial}{\partial x^l}_p)$on $Graph(F) = \{(a, F(a)); a \in V \}$

Published on 26 Mar 2026 - 17:53

List Question

Coordinate change of hypersurface differential form

Coordinate free covariant derivative of tensor densities

Comparing the definition for the pullback of generic vector bundles and the one for differential forms

Exercise 5.22 in the book Geometrical Methods of Mathematical Physics (by Bernard Schutz)

Show that a frame field is (not) holonomic - only possible by going to the coframe?

On the conclusion of the (compact) de Rham cohomology of $\mathbb{R}$

Lefschetz operator on bundle-valued forms

What exactly does "outward normal vector" means when talking about an orientation?

Riemann Roch Canonical Divisor - show the divisor of a differential form does not depend on choice of local coordinates

Deligne complex and sheaf of chain complex

Relation between trilinear forms, Jacobi identity and closed $2$-forms

Let $\{e^1,...,e^m\}$ standard basis of $(\Bbb R^m)^*$ , $(U,\varphi)$ a chart. Why is $d(x^i\circ \varphi^{-1})_{\varphi(p)}=d(e^i)_{\phi(p)}=e^i$?

Decomposition of 1-forms in simply connected open subset of Euclidean space

Why aren't integrals invariant over coordinate transformations?

Computing $ι^∗(dy^j)_p( \frac{\partial}{\partial x^l}_p)$ and $ι^∗(dz^k)_p( \frac{\partial}{\partial x^l}_p)$on $Graph(F) = \{(a, F(a)); a \in V \}$

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