Geodesic
Odd symmetric tensors, and an analogue of the Levi-Civita connection for odd symplectic structure
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2016), pp. 25-31

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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.
Keywords: half-density, odd (anti)symmetric tensor, second order compensation field, odd symplectic geometry, odd canonical operator.
Mots-clés : odd Poisson bracket, Cartan prolongation 
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H. M. Khudaverdian; M. Peddie. Odd symmetric tensors, and an analogue of the Levi-Civita connection for odd symplectic structure. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2016), pp. 25-31. http://geodesic.mathdoc.fr/item/UZERU_2016_3_a4/