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Abstract: We analyze from a general perspective all possible supersymmetricgeneralizations of symplectic and metric structures on smooth manifolds. Thereare two different types of structures according to the even-odd character ofthe corresponding quadratic tensors. In general we can have even-odd symplecticsupermanifolds, Fedosov supermanifolds and Riemannian supermanifolds. Thegeometry of even Fedosov supermanifolds is strongly constrained and has to beflat. In the odd case, the scalar curvature is only constrained by Bianchiidentities. However, we show that odd Riemannian supermanifolds can only haveconstant scalar curvature. We also point out that the supersymmetricgeneralizations of AdS space do not exist in the odd case.



Autor: M. Asorey, P.M. Lavrov

Fuente: https://arxiv.org/







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