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Integration of $\mathbb{d}\mathbb{d}^{*}+\mathbb{d}^{*}\mathbb{d}$ on manifolds with boundary

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#differential-geometry #manifolds #differential-forms
113
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Generator of $H^1(S^1)$ via integration of a bump $1$-form on $S^1$

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#algebraic-topology #differential-topology #differential-forms #de-rham-cohomology
61
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local expression of bundle valued differential forms

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#differential-geometry #differential-forms #vector-bundles
100
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Example of two different contact forms with the same Reeb vector field and exterior derivative.

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#tensors #differential-forms #symplectic-geometry #contact-geometry
43
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Reconciling two definitions of a differential form

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#differential-geometry #smooth-manifolds #differential-forms
111
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Understanding differential forms on manifolds (Bachman example 52)

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#differential-geometry #differential-forms
151
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Dual vector spaces - differential forms

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#differential-forms #exterior-derivative
464
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Use Stokes Theorem to Prove Cauchy Integral Formula

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#complex-analysis #differential-forms #stokes-theorem
64
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Let $z=a e^t$ then $dz=ae^tdt$, How to define $d \overline{z}=?$

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#complex-analysis #geometry #manifolds #differential-forms #complex-manifolds
40
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Stokes' theorem: what must the boundary satisfy

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#differential-forms #stokes-theorem
75
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Difficulty in proving $i_{\alpha} (\vartheta \wedge \zeta) = i_{\alpha} \vartheta \wedge \zeta + (-1)^k \vartheta \wedge i_{\alpha} \zeta.$

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#differential-geometry #smooth-manifolds #differential-forms #vector-fields #exterior-algebra
70
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Counterexample of a space where the wedge product of harmonic forms is not harmonic

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#differential-geometry #riemannian-geometry #differential-forms #harmonic-functions
91
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Is it possible to take an integral with respect to a vector?

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#integration #functions #vector-analysis #differential-forms
57
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How to inverse a gradient?

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#differential-geometry #differential-forms #differential-operators
53
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Elementary question on wedging 2-forms

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#differential-geometry #differential-forms #symplectic-geometry

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