2010/01/29 by Erik van Erp, van Erp, Erik · 1 citation
Mathematics · #46L85 #58J40 #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.1001.5426
openalex publication_date 2010/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A contact manifold is a manifold equipped with a distribution of codimension one that satisfies a `maximal non-integrability' condition. A standard example of a contact structure is a strictly pseudoconvex CR manifold, and operators of analytic interest are the tangential Cauchy-Riemann operator and the Szego projector onto its kernel. The Heisenberg calculus is the natural pseudodifferential calculus developed originally for the analysis of these operators. We introduce a `non-integrability' condition for a distribution of arbitrary codimension that directly generalizes the definition of a contact structure. We call such distributions polycontact structures. We prove that the polycontact condition is equivalent to the existence of generalized Szego projections in the Heisenberg calculus, and explore geometrically interesting examples of polycontact structures.