Fedosov supermanifolds: Basic properties and the difference in even and odd cases

Details Fedosov supermanifolds: Basic properties and the difference in even and odd cases Fedosov supermanifolds: Basic properties and the difference in even and odd cases

2003-06-23

arxiv.org/abs/hep-th/0306218v1

Int.J.Mod.Phys. A19 (2004) 3195-3208

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, Latex

Scientific paper

10.1142/S0217751X04018130

We study basic properties of supermanifolds endowed with an even (odd) symplectic structure and a connection respecting this symplectic structure. Such supermanifolds can be considered as generalization of Fedosov manifolds to the supersymmetric case. Choosing an apporpriate definition of inverse (second-rank) tensor fields on supermanifolds we consider the symmetry behavior of tensor fields as well as the properties of the symplectic curvature and of the Ricci tensor on even (odd) Fedosov supermanifolds. We show that for odd Fedosov supermanifolds the scalar curvature, in general, is non-trivial while for even Fedosov supermanifolds it necessarily vanishes.

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