Getzler's symbol calculus and the composition of differential operators on contact Riemannian manifolds

Abstract

Following Getzler's idea from the geometric viewpoint as to symbol calculus on a spin manifold, we introduce a new symbol calculus of $H$-pseudodifferential operators on a contact Riemannian manifold with contact distribution $H$. An explicit formula for the top grading part of the symbol of the composite of $H$-differential operators is presented.