Fedosov and Riemannian supermanifolds

Details Fedosov and Riemannian supermanifolds Fedosov and Riemannian supermanifolds

2008-03-11

arxiv.org/abs/0803.1591v1

J.Math.Phys.50:013530,2009

Physics

High Energy Physics

High Energy Physics - Theory

20 pages

Scientific paper

10.1063/1.3054867

Generalizations 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.

Affiliated with

Also associated with

No associations

Rating

Fedosov and Riemannian supermanifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fedosov and Riemannian supermanifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fedosov and Riemannian supermanifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-285947