Symplectic scalar curvatures on supermanifolds
Presented by Dr. Jose Antonio VALLEJO
Type: Oral presentation
Track: Diferential Geometry and Mathematical Physics
In Riemannian geometry, scalar curvature is introduced starting from the Riemann curvature tensor associated to a connection, by taking two successive contractions with respect to a metric compatible with the given connection. This contraction process could be (in principle) done with any 2-covariant non-degenerate tensor, compatible with the connection, and such that it has a geometrical interest; a symplectic form, for instance. However, the combined symmetries of the Riemann tensor and the symplectic form lead to a trivial situation. In symplectic supermanifolds, these difficulties are no longer present for a certain class of symplectic superforms, and the structure which arises (a Fedosov supermanifold) is very interesting from a physical point of view. In the talk, I will define the odd symplectic scalar curvature for these supermanifolds, and discuss their physical relevance.