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

Andrew James Bruce

Archivum Mathematicum (2020)

  • Volume: 056, Issue: 3, page 153-170
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Bruce, Andrew James. "Modular Classes of Q-Manifolds, Part II: Riemannian Structures $\&$ Odd Killing Vectors Fields." Archivum Mathematicum 056.3 (2020): 153-170. <http://eudml.org/doc/297194>.

@article{Bruce2020,
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.},
author = {Bruce, Andrew James},
journal = {Archivum Mathematicum},
keywords = {Q-manifolds; Riemannian supermanifolds; Killing vector fields; modular classes},
language = {eng},
number = {3},
pages = {153-170},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Modular Classes of Q-Manifolds, Part II: Riemannian Structures $\&$ Odd Killing Vectors Fields},
url = {http://eudml.org/doc/297194},
volume = {056},
year = {2020},
}

TY - JOUR
AU - Bruce, Andrew James
TI - Modular Classes of Q-Manifolds, Part II: Riemannian Structures $\&$ Odd Killing Vectors Fields
JO - Archivum Mathematicum
PY - 2020
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 056
IS - 3
SP - 153
EP - 170
AB - 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.
LA - eng
KW - Q-manifolds; Riemannian supermanifolds; Killing vector fields; modular classes
UR - http://eudml.org/doc/297194
ER -

References

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