Manchester Geometry Seminar 2013/2014

Thursday 13 February 2014. The Frank Adams Room (Room 1.212), the Alan Turing Building. 4.15pm

Differential Operators and Riemannian Curl on Contact Manifolds

Valentin Ovsienko (University of Reims)

We consider differential operators between sections of arbitrary powers of the determinant of the tangent bundle of a contact manifold. We show that there is an intrinsically defined "subsymbol" of a differential operator, which is a differential invariant of degree one lower than that of the principal symbol. In particular, this subsymbol associates a contact vector field to an arbitrary second order linear differential operator. For a contact manifold with a pseudo-Riemannian metric we obtain a contact vector field intrinsically associated to this pair of structures. We call this new differential invariant the contact Riemannian curl.