Vanishing and conservativeness of harmonic forms of a non-compact CR manifold

Abstract

The self-adjointness of a sublaplacian and Kohn-Rossi laplacians on a non-compact strictly pseudoconvex CR manifold is proved. As applications to geometry, the vanishing and the conservativeness of harmonic forms are obtained.

The Serre duality theorem for a non-compact weighted CR manifold

“…Since the proof is similar to the case where η ≡ 1 and E is trivial (e.g. [13]), we will omit the proof here.…”

“…Due to the HopfRinow theorem, H(n) is Riemannian complete, and we conclude by Proposition 5.1 that H(n) is complete. Moreover, it was proved in [13] that H p,q (E) = 0 for 0 < q < n − 1 when E is the trivial bundle over H(n). (1) A lens space…”

“…CR manifold was extended to a general s.p.c. CR manifold with negligible boundary (Definition 2.4) when E is a trivial line bundle by the second author [13].…”