Special Kähler-Ricci potentials on compact Kähler manifolds

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dc.creatorDerdzinski, A.
dc.creatorMaschler, G.
dc.date2002-04-27
dc.date.accessioned2026-07-07T06:29:50Z
dc.date.available2026-07-07T06:29:50Z
dc.descriptionA special Kähler-Ricci potential on a Kähler manifold is any nonconstant $C^\infty$ function $τ$ such that $J(\nablaτ)$ is a Killing vector field and, at every point with $dτ\ne 0$, all nonzero tangent vectors orthogonal to $\nablaτ$ and $J(\nablaτ)$ are eigenvectors of both $\nabla dτ$ and the Ricci tensor. For instance, this is always the case if $τ$ is a nonconstant $C^\infty$ function on a Kähler manifold $(M,g)$ of complex dimension $m>2$ and the metric $\tilde g=g/τ^2$, defined wherever $τ\ne 0$, is Einstein. (When such $τ$ exists, $(M,g)$ may be called {\it almost-everywhere conformally Einstein}.) We provide a complete classification of compact Kähler manifolds with special Kähler-Ricci potentials and use it to prove a structure theorem for compact Kähler manifolds of any complex dimension $m>2$ which are almost-everywhere conformally Einstein.
dc.description45 pages, AMSTeX, submitted to Journal für die reine und angewandte Mathematik
dc.identifierhttps://arxiv.org/abs/math/0204328
dc.identifierhttp://arxiv.org/abs/math/0204328
dc.identifierJ. reine angew. Math. 593 (2006), 73-116
dc.identifierdoi:10.1515/CRELLE.2006.030
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98181
dc.subjectDifferential Geometry
dc.subjectPrimary 53C55, 53C21 (Primary) 53C25 (Secondary)
dc.titleSpecial Kähler-Ricci potentials on compact Kähler manifolds
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