About: Kähler identities

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Attributes	Values
rdfs:label	Kähler identities (en)
name	Kähler identities (en) Hard Lefschetz decomposition (en)
dcterms:subject	Complex manifolds Differential geometry
Wikipage page ID	72163862 (xsd:integer)
Wikipage revision ID	1120450693 (xsd:integer)
Link from a Wikipage to another Wikipage	Hard Lefschetz theorem Ddbar lemma De Rham cohomology Complex manifolds Hodge star operator Holomorphic vector bundle Curvature form Differential geometry Commutator Compactly supported Nakano inequalities Hodge-Riemann bilinear relations Representation theory of SU(2) André Weil Lie algebra Bochner–Kodaira–Nakano identity Complex differential form Complex geometry Dolbeault operator W. V. D. Hodge Dolbeault cohomology Ample line bundle Exterior derivative Kodaira vanishing theorem Lefschetz hyperplane theorem Laplace operator Laplacian Hodge index theorem Hodge theory Solomon Lefschetz Special linear Lie algebra Tensorial Inner product Integration by parts Kodaira–Nakano vanishing theorem Kähler manifold Orientability Self-adjoint operator Hermitian metric Sl2-triple Hodge decomposition Kähler form Flat connection Laplace–de Rham operator Almost complex structure Chern connection Formal adjoint Hermitian vector bundle Adjoint operator dbr:Twisted_de_Rham_cohomology_group
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:Rp dbt:Math_theorem
math statement	Let be a compact Kähler manifold. Then the de Rham cohomology of admits an orthogonal direct sum decomposition This decomposition is compatible with the Hodge decomposition into Dolbeault cohomology groups: In addition * If , then . * The map is injective for , and restricts to give an injection for each such that . * The map is bijective for , and restricts to give a bijection for each such that . * If , then , and furthermore . (en) Let be a Kähler manifold. Then the following identities hold: * . * . . . * . * . * . . . * commutes with all of and . It also commutes with and hence preserves bidegree . Furthermore the operators and satisfy the identities: * . * . * . * . (en)
prov:wasDerivedFrom	wikipedia-en:Kähler_identities?oldid=1120450693&ns=0
page length (characters) of wiki page	22767 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Kähler_identities
is Link from a Wikipage to another Wikipage of	Primitive cohomology Ddbar lemma Nakano inequalities Hodge theory Kähler manifold
is Wikipage redirect of	Primitive cohomology Nakano inequalities
is foaf:primaryTopic of	wikipedia-en:Kähler_identities

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