  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.
