ODD SYMMETRIC TENSORS, AND AN ANALOGUE OF THE LEVI-CIVITA CONNECTION FOR ODD SYMPLECTIC STRUCTURE

H.M. Khudaverdian; M. Peddie

doi:10.46991/PYSU:A/2016.50.3.025

ODD SYMMETRIC TENSORS, AND AN ANALOGUE OF THE LEVI-CIVITA CONNECTION FOR ODD SYMPLECTIC STRUCTURE

Authors

H.M. Khudaverdian School of Mathematics, The University of Manchester, UK
M. Peddie School of Mathematics, The University of Manchester, UK

DOI:

https://doi.org/10.46991/PYSU:A/2016.50.3.025

Keywords:

odd Poisson bracket, half-density, odd (anti)symmetric tensor, Cartan prolongation, second order compensation field, odd symplectic geometry, odd canonical operator

Abstract

We consider odd Poisson (odd symplectic) structure on supermanifolds induced by an odd symmetric rank 2 (non-degenerate) contravariant tensor field. We describe the difference between odd Riemannian and odd symplectic structure in terms of the Cartan prolongation of the corresponding Lie algebras, and formulate an analogue of the Levi- Civita theorem for an odd symplectic supermanifold.

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Published

2016-10-26

How to Cite

Khudaverdian, H., & Peddie, M. (2016). ODD SYMMETRIC TENSORS, AND AN ANALOGUE OF THE LEVI-CIVITA CONNECTION FOR ODD SYMPLECTIC STRUCTURE. Proceedings of the YSU A: Physical and Mathematical Sciences, 50(3 (241), 25–31. https://doi.org/10.46991/PYSU:A/2016.50.3.025