2003/01/09 by A. Rod Gover, Gover, A. Rod, C. Robin Graham +1 · 2 citations
Mathematics · #32V05 (Primary) 53C07 #53B15 (Secondary) #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.DG #msc:32V05 #msc:53B15 #msc:53C07
paper · pdf · doi:10.48550/arxiv.math/0301092
31 pages
arxiv created 2003/01/09 · openalex publication_date 2003/01/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
CR invariant differential operators on densities with leading part a power of the sub-Laplacian are derived. One family of such operators is constructed from the ``conformally invariant powers of the Laplacian'' via the Fefferman metric; the powers which arise for these operators are bounded in terms of the dimension. A second family is derived from a CR tractor calculus which is developed here; this family includes operators for every positive power of the sub-Laplacian. This result together with work of Cap, Slovak and Soucek imply in three dimensions the existence of a curved analogue of each such operator in flat space.