# 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)

ovsienko@math.univ-lyon1.fr

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.