A class of compact Poincare-Einstein manifolds: properties and construction

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dc.creatorGover, A. Rod
dc.creatorLeitner, Felipe
dc.date2008-08-15
dc.date.accessioned2026-07-07T09:56:52Z
dc.date.available2026-07-07T09:56:52Z
dc.descriptionWe develop a geometric and explicit construction principle that generates classes of Poincare-Einstein manifolds, and more generally almost Einstein manifolds. Almost Einstein manifolds satisfy a generalisation of the Einstein condition; they are Einstein on an open dense subspace and, in general, have a conformal scale singularity set that is a conformal infinity for the Einstein metric. In particular, the construction may be applied to yield families of compact Poincare-Einstein manifolds, as well as classes of almost Einstein manifolds that are compact without boundary. We obtain classification results which show that the construction essentially exhausts a class of almost Einstein (and Poincare-Einstein) manifold. We develop the general theory of fixed conformal structures admitting multiple compatible almost Einstein structures. We also show that, in a class of cases, these are canonically related to a family of constant mean curvature totally umbillic embedded hypersurfaces.
dc.description28 pages
dc.identifierhttps://arxiv.org/abs/0808.2097
dc.identifierhttp://arxiv.org/abs/0808.2097
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167137
dc.subjectDifferential Geometry
dc.subjectMathematical Physics
dc.subject53C25, 53A30 (Primary); 53B20 (Secondary)
dc.titleA class of compact Poincare-Einstein manifolds: properties and construction
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