A new hypoelliptic operator on almost CR manifolds

Abstract

The aim of this paper is to present the construction, out of the Kohn-Rossi complex, of a new hypoelliptic operator Q L on almost CR manifolds equipped with a real structure. The operator acts on all (p, q)-forms, but when restricted to (p, 0)-forms and (p, n)-forms it is a sum of squares up to sign factor and lower order terms. Therefore, only a finite type condition condition is needed to have hypoellipticity on those forms. However, outside these forms Q L may fail to be hypoelliptic, as it is shown in the example of the Heisenberg group H 5 .