Riemannian Supergeometry

Details Riemannian Supergeometry Riemannian Supergeometry

2006-04-06

arxiv.org/abs/math/0604143v1

Math. Z. 260 (2008), no. 3, 557-593

Mathematics

Differential Geometry

43 pages, abridged version of author's thesis

Scientific paper

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.

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