List questions from differential-forms

186

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Compute the degree of $\phi:(x_1,x_2,x_3,x_4) \mapsto (x_1,-x_3,-x_2,x_4)$. Does $\phi$ preserve orientation?

Published on 27 Mar 2026 - 1:47

151

Views

Basis representation of differential-form $f(x_1,x_2):=(x_1+x_2, -x_1, -x_2)^T$

Published on 09 Feb 2016 - 14:20

128

Views

How to calculate $f(x, y, z)$ given $d f = \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial y} dy +\frac{\partial f}{\partial z} dz$

Published on 10 Feb 2016 - 0:30

38

Views

Find $f \in C^1(U,\mathbb{R})$ which satisfiyes the following differential-form

Published on 10 Feb 2016 - 15:45

230

Views

Constructing the Hodge Laplacian from the Laplace-Beltrami one

Published on 31 Mar 2026 - 14:18

771

Views

Closed Form and Pullback compatibility

Published on 11 Feb 2016 - 11:52

249

Views

Boundary of a $k-$Cell Definition

Published on 12 Feb 2016 - 5:28

66

Views

matrix valued integrating factor of one forms (reference request)

Published on 12 Feb 2016 - 18:21

349

Views

Where is the error in this proof of the Hodge theorem?

Published on 23 Feb 2026 - 15:47

3.5k

Views

necessary and sufficient condition for the lines of curvature

Published on 30 Mar 2026 - 21:44

683

Views

Complex Analysis with differential forms

Published on 01 Apr 2026 - 7:49

67

Views

How can I solve this difference equation, if $p=q$?

Published on 27 Mar 2026 - 0:07

109

Views

When is a $(p,q)$-form real?

Published on 16 Feb 2016 - 13:32

607

Views

Can a closed differential form on a subset of manifold always be extended to the whole manifold?

Published on 18 Feb 2016 - 17:32

258

Views

Differential forms on a scheme: unclear equation

Published on 20 Feb 2016 - 3:40

List Question

Compute the degree of $\phi:(x_1,x_2,x_3,x_4) \mapsto (x_1,-x_3,-x_2,x_4)$. Does $\phi$ preserve orientation?

Basis representation of differential-form $f(x_1,x_2):=(x_1+x_2, -x_1, -x_2)^T$

How to calculate $f(x, y, z)$ given $d f = \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial y} dy +\frac{\partial f}{\partial z} dz$

Find $f \in C^1(U,\mathbb{R})$ which satisfiyes the following differential-form

Constructing the Hodge Laplacian from the Laplace-Beltrami one

Closed Form and Pullback compatibility

Boundary of a $k-$Cell Definition

matrix valued integrating factor of one forms (reference request)

Where is the error in this proof of the Hodge theorem?

necessary and sufficient condition for the lines of curvature

Complex Analysis with differential forms

How can I solve this difference equation, if $p=q$?

When is a $(p,q)$-form real?

Can a closed differential form on a subset of manifold always be extended to the whole manifold?

Differential forms on a scheme: unclear equation

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