Fedosov and Riemannian supermanifolds

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dc.creatorAsorey, M.
dc.creatorLavrov, P. M.
dc.date2008-03-11
dc.date.accessioned2026-07-07T12:39:04Z
dc.date.available2026-07-07T12:39:04Z
dc.descriptionGeneralizations of symplectic and metric structures for supermanifolds are analyzed. Two types of structures are possible according to the even/odd character of the corresponding quadratic tensors. In the even case one has a very rich set of geometric structures: even symplectic supermanifolds (or, equivalently, supermanifolds with non-degenerate Poisson structures), even Fedosov supermanifolds and even Riemannian supermanifolds. The existence of relations among those structures is analyzed in some details. In the odd case, we show that odd Riemannian and Fedosov supermanifolds are characterized by a scalar curvature tensor. However, odd Riemannian supermanifolds can only have constant curvature.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/0803.1591
dc.identifierhttp://arxiv.org/abs/0803.1591
dc.identifierJ.Math.Phys.50:013530,2009
dc.identifierdoi:10.1063/1.3054867
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/218983
dc.subjectHigh Energy Physics - Theory
dc.titleFedosov and Riemannian supermanifolds
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