  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.
