List questions from differential-forms

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Reading recommendation for the chapter 4 of Spivak's Calculus on Manifolds

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Smooth 1-forms and smooth sections

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Understanding the definition of exterior derivative

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Bianchi Identity in Chern's book

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Hamilton equations by flow of Hamiltonian vector field

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How to linearly extend the DeRahm operator $d \colon \Omega^{}(M) \to \Omega^{+1}(M) $

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given a closed $1$-form $\alpha$, find $0$-form $f$ s.t. $df = \alpha$.

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Integration along fibers

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Prove that the integral of a differential form on an open set is well defined.

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Explicit expression of the operator $d^*d$ on 1-forms

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Calculating divergence for parabolic coordinates.

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Proof that closed forms are exact using Stokes' theorem.

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Is this definition of the gradient using the exterior derivative consistent with calculus 1?

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How does one interpret this functional and its sign?

Published on 11 Apr 2026 - 3:31

List Question

The differential complex of smooth forms

Reading recommendation for the chapter 4 of Spivak's Calculus on Manifolds

Smooth 1-forms and smooth sections

Understanding the definition of exterior derivative

Bianchi Identity in Chern's book

Hamilton equations by flow of Hamiltonian vector field

How to linearly extend the DeRahm operator $d \colon \Omega^{}(M) \to \Omega^{+1}(M) $

given a closed $1$-form $\alpha$, find $0$-form $f$ s.t. $df = \alpha$.

Integration along fibers

Prove that the integral of a differential form on an open set is well defined.

Explicit expression of the operator $d^*d$ on 1-forms

Calculating divergence for parabolic coordinates.

Proof that closed forms are exact using Stokes' theorem.

Is this definition of the gradient using the exterior derivative consistent with calculus 1?

How does one interpret this functional and its sign?

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