Para-Hermitian and Para-Quaternionic manifolds

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dc.creatorIvanov, Stefan
dc.creatorZamkovoy, Simeon
dc.date2003-10-26
dc.date2005-07-06
dc.date.accessioned2026-07-07T06:23:45Z
dc.date.available2026-07-07T06:23:45Z
dc.descriptionA set of canonical parahermitian connections on an almost paraHermitian manifold is defined. ParaHermitian version of the Apostolov-Gauduchon generalization of the Goldberg-Sachs theorem in General Relativity is given. It is proved that the Nijenhuis tensor of a Nearly paraKähler manifolds is parallel with respect to the canonical connection. Salamon's twistor construction on quaternionic manifold is adapted to the paraquaternionic case. A hyper-paracomplex structure is constructed on Kodaira-Thurston (properly elliptic) surfaces as well as on the Inoe surfaces modeled on $Sol^4_1$. A locally conformally flat hyper-paraKähler (hypersymplectic) structure with parallel Lee form on Kodaira-Thurston surfaces is obtained. Anti-self-dual non-Weyl flat neutral metric on Inoe surfaces modeled on $Sol^4_1$ is presented. An example of anti-self-dual neutral metric which is not locally conformally hyper-paraKähler is constructed.
dc.descriptionLaTeX2e, 27 pages, final version, to appear in Diff. Geom. Appl
dc.identifierhttps://arxiv.org/abs/math/0310415
dc.identifierhttp://arxiv.org/abs/math/0310415
dc.identifierDiffer.Geom.Appl. 23 (2005) 205-234
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96347
dc.subjectDifferential Geometry
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subject53C15
dc.titlePara-Hermitian and Para-Quaternionic manifolds
dc.typetext

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