By Dmitri V. Alekseevsky and Helga Baum, Dmitri V. Alekseevsky
This booklet presents an advent to and survey of modern advancements in pseudo-Riemannian geometry, together with purposes in mathematical physics, by way of best specialists within the box. issues coated are: category of pseudo-Riemannian symmetric areas Holonomy teams of Lorentzian and pseudo-Riemannian manifolds Hypersymplectic manifolds Anti-self-dual conformal buildings in impartial signature and integrable structures impartial Kahler surfaces and geometric optics Geometry and dynamics of the Einstein universe crucial conformal constructions and conformal ameliorations in pseudo-Riemannian geometry The causal hierarchy of spacetimes Geodesics in pseudo-Riemannian manifolds Lorentzian symmetric areas in supergravity Generalized geometries in supergravity Einstein metrics with Killing leaves The publication is addressed to complicated scholars in addition to to researchers in differential geometry, worldwide research, common relativity and string idea. It indicates crucial changes among the geometry on manifolds with confident certain metrics and on people with indefinite metrics, and highlights the fascinating new geometric phenomena, which certainly come up within the indefinite metric case. The reader reveals an outline of the current cutting-edge within the box in addition to open difficulties, which could stimulate extra study.