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Quasi-Einstein structures on a surface

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TWT - Twistor theory

A quasi-Einstein manifold is a Riemannian manifold together with a vector field satisfying a system of equations generalising the Einstein equations. Special cases include the near horizon equation arising on spatial cross sections of extremal black hole horizons in general relativity, as well as connections to projective metrizability and Einstein-Weyl structures.   This talk will focus on the two-dimensional case. We derive all axially symmetric quasi-Einstein structures on the sphere. We also discuss the link to the problem of finding all projective classes that are both metrizable and skew. In two dimensions the corresponding quasi-Einstein structures arise as symmetry reductions of the anti-self-dual Yang-Mills equations and can be identified with Hitchin equations.    

This talk is part of the Isaac Newton Institute Seminar Series series.

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