Modular Classes of Q-Manifolds, Part II: Riemannian Structures & Odd Killing Vectors Fields

Abstract

We define and make an initial study of (even) Riemannian supermanifolds equipped with a homological vector field that is also a Killing vector field. We refer to such supermanifolds as Riemannian Q-manifolds. We show that such Q-manifolds are unimodular, i.e., come equipped with a Q-invariant Berezin volume.

arXiv comment12 pages. This preprint is a continuation of an earlier paper by the author published as Archivum Mathematicum, vol. 53 (2017), issue 4, pp. 203-219

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