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arXiv · 1205.6562

Linear differential operators on contact manifolds

Charles H. Conley·Valentin Ovsienko
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Abstract

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.

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Charles H. Conley, Valentin Ovsienko. 2012-05-30. Linear differential operators on contact manifolds. https://doi.org/10.1093/imrn%2Frnv364

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