35,051 research outputs found
Linear differential operators on contact manifolds
We consider differential operators between sections of arbitrary powers of
the determinant line bundle over a contact manifold. We extend the standard
notions of the Heisenberg calculus: noncommutative symbolic calculus, the
principal symbol, and the contact order to such differential operators. Our
first main result 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. Our second
main result is the construction of a filtration that strengthens the well-known
contact order filtration of the Heisenberg calculus
- …