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Riemannian Supergeometry

Research paper by Oliver Goertsches

Indexed on: 06 Apr '06Published on: 06 Apr '06Published in: Mathematics - Differential Geometry



Abstract

Motivated by a paper of Zirnbauer, we develop a theory of Riemannian supermanifolds up to a definition of Riemannian symmetric superspaces. Various fundamental concepts needed for the study of these spaces both from the Riemannian and the Lie theoretical viewpoint are introduced, e.g. geodesics, isometry groups and invariant metrics on Lie supergroups and homogeneous superspaces.