Penn Arts & Sciences Logo

Geometry-Topology Seminar

Thursday, April 11, 2002 - 4:30pm

Aissa Wade

Penn State University

Location

University of Pennsylvania

DRL 4C8

Abstract: A Jacobi structure on a smooth manifold is a local Lie algebra structure in the sense of Kirillov. This is equivalent to the existence of a pair formed by a skew-symmetric contravariant 2-tensor field and a vector field, which satisfy some compatibility conditions expressed in terms of the Schouten-Nijenhuis bracket, as shown by Lichnerowicz. The class of Jacobi manifolds includes symplectic, contact and Poisson manifolds. An alternative approach to Poisson and contact manifolds is the theory of Dirac structures, which has been introduced by Courant and Weinstein. In this talk, I will present a characterization of Jacobi structures through the theory of Dirac structures. Also, I will discuss recent results concerning some aspects of the generalized foliation arising from a Jacobi structure.