Einstein-Weyl structures on complex manifolds and conformal version of Monge-Ampere equation

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dc.creatorOrnea, Liviu
dc.creatorVerbitsky, Misha
dc.date2006-06-13
dc.date2008-08-01
dc.date.accessioned2026-07-07T12:32:14Z
dc.date.available2026-07-07T12:32:14Z
dc.descriptionA Hermitian Einstein-Weyl manifold is a complex manifold admitting a Ricci-flat Kaehler covering W, with the deck transform acting on W by homotheties. If compact, it admits a canonical Vaisman metric, due to Gauduchon. We show that a Hermitian Einstein-Weyl structure on a compact complex manifold is determined by its volume form. This result is a conformal analogue of Calabi's theorem stating the uniqueness of Kaehler metrics with a given volume form in a given Kaehler class. We prove that a solution of a conformal version of complex Monge-Ampere equation is unique. We conjecture that a Hermitian Einstein-Weyl structure on a compact complex manifold is unique, up to a holomorphic automorphism, and compare this conjecture to Bando-Mabuchi theorem.
dc.description17 pages, v. 3.0: another error corrected
dc.identifierhttps://arxiv.org/abs/math/0606309
dc.identifierhttp://arxiv.org/abs/math/0606309
dc.identifierBull. Math. Soc. Sci. Math. Roumanie (N.S.) 51(99) (2008), no. 4, 339--353.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216713
dc.subjectComplex Variables
dc.subjectAlgebraic Geometry
dc.subjectDifferential Geometry
dc.titleEinstein-Weyl structures on complex manifolds and conformal version of Monge-Ampere equation
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