Almost Einstein and Poincare-Einstein manifolds in Riemannian signature - Mathematics > Differential GeometryReportar como inadecuado




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Abstract: An almost Einstein manifold satisfies equations which are a slight weakeningof the Einstein equations; Einstein metrics, Poincare-Einstein metrics, andcompactifications of certain Ricci-flat asymptotically locally Euclideanstructures are special cases. The governing equation is a conformally invariantoverdetermined PDE on a function. Away from the zeros of this the almostEinstein structure is Einstein, while the zero set gives a scale singularityset which may be viewed as a conformal infinity for the Einstein metric. Inthis article we give a classification of the possible scale singularity spacesand derive geometric results which explicitly relate the intrinsic conformalgeometry of these to the conformal structure of the ambient almost Einsteinmanifold. Classes of examples are constructed. A compatible generalisation ofthe constant scalar curvature condition is also developed. This includes almostEinstein as a special case, and when its curvature is suitably negative, isclosely linked to the notion of an asymptotically hyperbolic structure.



Autor: A. Rod Gover

Fuente: https://arxiv.org/







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