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

Andrew James Bruce

Address: Mathematics Research Unit, University of Luxembourg, Maison du Nombre 6, avenue de la Fonte, L-4364 Esch-sur-Alzette

E-mail: andrewjamesbruce@googlemail.com

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.

AMSclassification: primary 17B66; secondary 57R20, 57R25, 58A50, 58B20.

Keywords: Q-manifolds, Riemannian supermanifolds, Killing vector fields, modular classes.

DOI: 10.5817/AM2020-3-153