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- Complex_differential_form abstract "In mathematics, a complex differential form is a differential form on a manifold (usually a complex manifold) which is permitted to have complex coefficients.Complex forms have broad applications in differential geometry. On complex manifolds, they are fundamental and serve as the basis for much of algebraic geometry, Kähler geometry, and Hodge theory. Over non-complex manifolds, they also play a role in the study of almost complex structures, the theory of spinors, and CR structures.Typically, complex forms are considered because of some desirable decomposition that the forms admit. On a complex manifold, for instance, any complex k-form can be decomposed uniquely into a sum of so-called (p,q)-forms: roughly, wedges of p differentials of the holomorphic coordinates with q differentials of their complex conjugates. The ensemble of (p,q)-forms becomes the primitive object of study, and determines a finer geometrical structure on the manifold than the k-forms. Even finer structures exist, for example, in cases where Hodge theory applies.".
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- Complex_differential_form wikiPageLength "6955".
- Complex_differential_form wikiPageOutDegree "31".
- Complex_differential_form wikiPageRevisionID "649552945".
- Complex_differential_form wikiPageWikiLink Algebraic_geometry.
- Complex_differential_form wikiPageWikiLink Almost_complex_manifold.
- Complex_differential_form wikiPageWikiLink Almost_complex_structure.
- Complex_differential_form wikiPageWikiLink CR_manifold.
- Complex_differential_form wikiPageWikiLink CR_structure.
- Complex_differential_form wikiPageWikiLink Category:Complex_manifolds.
- Complex_differential_form wikiPageWikiLink Category:Differential_forms.
- Complex_differential_form wikiPageWikiLink Cauchy-Riemann_equations.
- Complex_differential_form wikiPageWikiLink Cauchy–Riemann_equations.
- Complex_differential_form wikiPageWikiLink Complex_manifold.
- Complex_differential_form wikiPageWikiLink Complex_number.
- Complex_differential_form wikiPageWikiLink Coordinate_system.
- Complex_differential_form wikiPageWikiLink Differentiable_manifold.
- Complex_differential_form wikiPageWikiLink Differential_form.
- Complex_differential_form wikiPageWikiLink Differential_geometry.
- Complex_differential_form wikiPageWikiLink Differential_of_the_first_kind.
- Complex_differential_form wikiPageWikiLink Direct_sum_of_vector_bundles.
- Complex_differential_form wikiPageWikiLink Dolbeault_cohomology.
- Complex_differential_form wikiPageWikiLink Dolbeault_complex.
- Complex_differential_form wikiPageWikiLink Exterior_derivative.
- Complex_differential_form wikiPageWikiLink Frölicher_spectral_sequence.
- Complex_differential_form wikiPageWikiLink Hodge_theory.
- Complex_differential_form wikiPageWikiLink Holomorphic_function.
- Complex_differential_form wikiPageWikiLink Kähler_manifold.
- Complex_differential_form wikiPageWikiLink Kähler_metric.
- Complex_differential_form wikiPageWikiLink Manifold.
- Complex_differential_form wikiPageWikiLink Mathematics.
- Complex_differential_form wikiPageWikiLink Multi-index.
- Complex_differential_form wikiPageWikiLink Multi-index_notation.
- Complex_differential_form wikiPageWikiLink Sheaf_(mathematics).
- Complex_differential_form wikiPageWikiLink Smooth_manifold.
- Complex_differential_form wikiPageWikiLink Spinor.
- Complex_differential_form wikiPageWikiLink Tensor.
- Complex_differential_form wikiPageWikiLink Vector_bundle.
- Complex_differential_form wikiPageWikiLinkText "(''p'',''q'')-forms".
- Complex_differential_form wikiPageWikiLinkText "Complex differential form".
- Complex_differential_form wikiPageWikiLinkText "Complex differential form#The Dolbeault operators".
- Complex_differential_form wikiPageWikiLinkText "Dolbeault operators".
- Complex_differential_form wikiPageWikiLinkText "complex differential form".
- Complex_differential_form wikiPageWikiLinkText "complex differential form#The Dolbeault operators".
- Complex_differential_form wikiPageWikiLinkText "complex forms".
- Complex_differential_form wikiPageWikiLinkText "holomorphic 1-forms".
- Complex_differential_form hasPhotoCollection Complex_differential_form.
- Complex_differential_form wikiPageUsesTemplate Template:Cite_book.
- Complex_differential_form subject Category:Complex_manifolds.
- Complex_differential_form subject Category:Differential_forms.
- Complex_differential_form hypernym Form.
- Complex_differential_form type Article.
- Complex_differential_form type Article.
- Complex_differential_form type Tensor.
- Complex_differential_form type Variable.
- Complex_differential_form comment "In mathematics, a complex differential form is a differential form on a manifold (usually a complex manifold) which is permitted to have complex coefficients.Complex forms have broad applications in differential geometry. On complex manifolds, they are fundamental and serve as the basis for much of algebraic geometry, Kähler geometry, and Hodge theory.".
- Complex_differential_form label "Complex differential form".
- Complex_differential_form sameAs Komplexe_Differentialform.
- Complex_differential_form sameAs 複素微分形式.
- Complex_differential_form sameAs 복소수_미분_형식.
- Complex_differential_form sameAs m.07j109.
- Complex_differential_form sameAs Q1780913.
- Complex_differential_form sameAs Q1780913.
- Complex_differential_form wasDerivedFrom Complex_differential_form?oldid=649552945.
- Complex_differential_form isPrimaryTopicOf Complex_differential_form.