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

Abstract

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.

arXiv comment10 pages, Latex

References in corpus (1)

• Modified triplectic quantization in general coordinates

Cited by in corpus (12)

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• A note on the supersymplectic structure of triplextic formalism
• General quantum-mechanical setting for field-antifield formalism as a hyper-gauge theory
• Symplectic connections and Fedosov's quantization on supermanifolds
• Higher order relations in Fedosov supermanifolds
• Superfield extended BRST quantization in general coordinates
• Supermanifolds, symplectic geometry and curvature