About: Constant scalar curvature Kähler metric

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In differential geometry, a constant scalar curvature Kähler metric (cscK metric), is (as the name suggests) a Kähler metric on a complex manifold whose scalar curvature is constant. A special case is Kähler–Einstein metric, and a more general case is extremal Kähler metric.

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rdfs:label	Constant scalar curvature Kähler metric (en)
rdfs:comment	In differential geometry, a constant scalar curvature Kähler metric (cscK metric), is (as the name suggests) a Kähler metric on a complex manifold whose scalar curvature is constant. A special case is Kähler–Einstein metric, and a more general case is extremal Kähler metric. (en)
dcterms:subject	Complex manifolds
Wikipage page ID	37860980 (xsd:integer)
Wikipage revision ID	1040437751 (xsd:integer)
Link from a Wikipage to another Wikipage	Calabi Scalar curvature Mabuchi functional De Rham cohomology Complex manifolds Kähler–Einstein metric Kähler-Einstein metric Critical point (mathematics) Lie algebra Calabi flow Calabi–Yau manifold Smooth function Complex manifold K-stability Extremal Kähler metric Riemannian metric Hamiltonian vector field K-Stability Hermitian Yang–Mills connection Differential geometry Automorphism group Moment map Yang–Mills connection Yang–Mills functional Kähler metric Kähler potential Futaki invariant Einstein summation notation Holomorphic vector field dbr:Anti-self_dual_connection dbr:Kähler–Ricci_solitons
Link from a Wikipage to an external page	https://doi.org/10.4310/jdg/1090349449 https://doi.org/10.4310/jdg/1090950195
sameAs	Constant scalar curvature Kähler metric Constant scalar curvature Kähler metric Constant scalar curvature Kähler metric
dbp:wikiPageUsesTemplate	dbt:Citation dbt:Citation_needed dbt:Harvtxt dbt:Reflist
has abstract	In differential geometry, a constant scalar curvature Kähler metric (cscK metric), is (as the name suggests) a Kähler metric on a complex manifold whose scalar curvature is constant. A special case is Kähler–Einstein metric, and a more general case is extremal Kähler metric. , Tian and Yau conjectured that the existence of a cscK metric on a polarised projective manifold is equivalent to the polarised manifold being K-polystable. Recent developments in the field suggest that the correct equivalence may be to the polarised manifold being uniformly K-polystable. When the polarisation is given by the (anti)-canonical line bundle (i.e. in the case of Fano or Calabi–Yau manifolds) the notions of K-stability and K-polystability coincide, cscK metrics are precisely Kähler-Einstein metrics and the Yau-Tian-Donaldson conjecture is known to hold. (en)
gold:hypernym	Kähler
prov:wasDerivedFrom	wikipedia-en:Constant_scalar_curvature_Kähler_metric?oldid=1040437751&ns=0
page length (characters) of wiki page	7438 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Constant_scalar_curvature_Kähler_metric
is Link from a Wikipage to another Wikipage of	Mabuchi functional Quillen metric Complex geometry Toshiki Mabuchi K-stability Extremal Kähler metric Kobayashi–Hitchin correspondence Constant scalar curvature Kahler metric Kähler manifold Constant scalar curvature Kaehler metric Constant scalar curvature Kahler manifold Constant scalar curvature Kähler manifold CscK CscK manifold CscK metric Holomorphy potential
is Wikipage redirect of	Extremal Kähler metric Constant scalar curvature Kahler metric Constant scalar curvature Kaehler metric Constant scalar curvature Kahler manifold Constant scalar curvature Kähler manifold CscK CscK manifold CscK metric Holomorphy potential
is foaf:primaryTopic of	wikipedia-en:Constant_scalar_curvature_Kähler_metric

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