Geodesic
Modular Classes of Q-Manifolds, Part II: Riemannian Structures $\$ Odd Killing Vectors Fields
Archivum mathematicum, Tome 56 (2020) no. 3, pp. 153-170.

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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.
DOI : 10.5817/AM2020-3-153
Classification : 17B66, 57R20, 57R25, 58A50, 58B20
Keywords: Q-manifolds; Riemannian supermanifolds; Killing vector fields; modular classes 
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     title = {Modular {Classes} of {Q-Manifolds,} {Part} {II:} {Riemannian} {Structures} $\&$ {Odd} {Killing} {Vectors} {Fields}},
     journal = {Archivum mathematicum},
     pages = {153--170},
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Bruce, Andrew James. Modular Classes of Q-Manifolds, Part II: Riemannian Structures $\&$ Odd Killing Vectors Fields. Archivum mathematicum, Tome 56 (2020) no. 3, pp. 153-170. doi : 10.5817/AM2020-3-153. http://geodesic.mathdoc.fr/articles/10.5817/AM2020-3-153/

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