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تسجيل مستخدم جديدSymplectic geometries on supermanifolds
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Extension of symplectic geometry on manifolds to the supersymmetric case is considered. In the even case it leads to the even symplectic geometry (or, equivalently, to the geometry on supermanifolds endowed with a non-degenerate Poisson bracket) or to the geometry on an even Fedosov supermanifolds. It is proven that in the odd case there are two different scalar symplectic structures (namely, an odd closed differential 2-form and the antibracket) which can be used for construction of symplectic geometries on supermanifolds.
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We analyze from a general perspective all possible supersymmetric generalizations of symplectic and metric structures on smooth manifolds. There are two different types of structures according to the even/odd character of the corresponding quadratic
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