Odd symmetric tensors, and an analogue of the Levi-Civita connection for odd symplectic structure

Hovhannes Khudaverdyan; Matthew Peddie

Odd symmetric tensors, and an analogue of the Levi-Civita connection for odd symplectic structure

Hovhannes Khudaverdyan, Matthew Peddie

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Abstract

We consider odd Poisson (odd symplectic) structure on supermanifolds induced by an odd symmetric rank 22 (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.

Original language	English
Pages (from-to)	25–31
Journal	Proceedings of Yerevan State University Physical and Mathematical Sciences
Issue number	3
Publication status	Published - 1 Dec 2016

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abstract = "We consider odd Poisson (odd symplectic) structure on supermanifolds induced by an odd symmetric rank 22 (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. ",

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AB - We consider odd Poisson (odd symplectic) structure on supermanifolds induced by an odd symmetric rank 22 (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.

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Odd symmetric tensors, and an analogue of the Levi-Civita connection for odd symplectic structure

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