About: CR manifold

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In mathematics, a CR manifold, or Cauchy–Riemann manifold, is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an edge of a wedge. Formally, a CR manifold is a differentiable manifold M together with a preferred complex distribution L, or in other words a complex subbundle of the complexified tangent bundle such that * (L is formally integrable) * . The subbundle L is called a CR structure on the manifold M. The abbreviation CR stands for "Cauchy–Riemann" or "Complex-Real".

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rdf:type	Thing yago:WikicatSmoothManifolds yago:Artifact100021939 yago:Conduit103089014 yago:Manifold103717750 yago:Object100002684 yago:Passage103895293 yago:PhysicalEntity100001930 yago:Pipe103944672 yago:YagoGeoEntity yago:YagoPermanentlyLocatedEntity yago:Tube104493505 yago:Way104564698 yago:Whole100003553
rdfs:label	CR manifold (en) CR多様体 (ja)
rdfs:comment	In mathematics, a CR manifold, or Cauchy–Riemann manifold, is a differentiable manifold together with a geometric structure modeled on that of a real hypersurface in a complex vector space, or more generally modeled on an edge of a wedge. Formally, a CR manifold is a differentiable manifold M together with a preferred complex distribution L, or in other words a complex subbundle of the complexified tangent bundle such that * (L is formally integrable) * . The subbundle L is called a CR structure on the manifold M. The abbreviation CR stands for "Cauchy–Riemann" or "Complex-Real". (en) 数学において、CR多様体（CRたようたい、英: CR manifold）とは，微分可能多様体で，複素数空間の中の実超曲面の幾何構造をモデル化したものである． CR は，コーシー・リーマン，あるいは，複素 (Complex)・実 (Real) の省略形である． (ja)
dcterms:subject	Smooth manifolds Complex manifolds
Wikipage page ID	3131794 (xsd:integer)
Wikipage revision ID	1110783949 (xsd:integer)
Link from a Wikipage to another Wikipage	Hermitian form Smooth manifolds Complex manifolds Annali di Matematica Pura ed Applicata Holomorphic function Holomorphic functions Joseph J. Kohn Paul C. Yang Charles Epstein Vector field David Jerison Pseudoconvexity Convex set Mathematics Mei-Chi Shaw Tangent bundle André Lichnerowicz Louis Nirenberg Complex manifold Yum-Tong Siu François Trèves Dolbeault operator Heisenberg group Line bundle Stein manifold Aldo Andreotti Eugenio Elia Levi Exterior derivative Differential operator Dirichlet problem Kengo Hirachi Riemannian geometry H. Blaine Lawson Hans Grauert Hans Lewy Cotangent bundle Hypersurface Paneitz operator John M. Lee Laplace operator Cohomology Edge-of-the-wedge theorem Differentiable manifold C. Robin Graham Dolbeault complex Implicit function theorem Real number Complex coordinate space Yamabe problem Louis Boutet de Monvel Masatake Kuranishi Sesquilinear Exterior product Plurisubharmonic function Hermitian metric Subbundle Rauch comparison theorem Minimal surfaces Frobenius integration theorem Hörmander Cauchy–Riemann Sidney M. Webster Cohomology groups Bernstein problem Complexified Antiholomorphic Neumann problem dbr:CR_functions dbr:CR_pluriharmonic_functions dbr:Sagun_Chanillo dbr:Stephen_S.-T._Yau dbr:Sub-Laplacian dbr:Vector_valued_2-form
Link from a Wikipage to an external page	https://web.archive.org/web/20110605031221/http:/www.numdam.org/numdam-bin/fitem%3Fid=ASNSP_1995_4_22_2_315_0%7Carchive-date=2011-06-05%7Curl-status=dead https://zenodo.org/record/2269099 http://www.numdam.org/numdam-bin/fitem%3Fid=ASNSP_1995_4_22_2_315_0%7Ctitle=Duality
sameAs	CR manifold CR manifold

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