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Riemannian supergeometry

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Abstract

Motivated by Zirnbauer in J Math Phys 37(10):4986–5018 (1996), 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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Authors and Affiliations

  1. Department of Mathematics, University of California at Irvine, Irvine, CA, 92697-3875, USA

    O. Goertsches

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  1. O. Goertsches
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Correspondence to O. Goertsches.

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Research supported by the DFG, SFB TR/12 “Symmetries and Universality in Mesoscopic Systems”.

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Goertsches, O. Riemannian supergeometry. Math. Z. 260, 557–593 (2008). https://doi.org/10.1007/s00209-007-0288-z

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  • DOI: https://doi.org/10.1007/s00209-007-0288-z

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