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We consider odd Poisson (odd symplectic) structure on supermanifolds inducedby an odd symmetric rank $2$ (non-degenerate) contravariant tensor field. Wedescribe the difference between odd Riemannian and odd symplectic structure interms of the Cartan prolongation of the corresponding Lie algebras, andformulate an analogue of the Levi-Civita theorem for an odd symplecticsupermanifold.

Odd Symmetric Tensors, and an Analogue of the Levi-Civita Connection for an Odd Symplectic Supermanifold