Vanishing and conservativeness of harmonic forms of a non-compact CR manifold
The paper under review is a tentative to derive 1) a Bochner type formula on a strictly pseudoconvex CR manifold \(M\) and consequently a result on the vanishing of the Kohn-Rossi cohomology groups of \(M\), presumably in the presence of an assumption on the pseudohermitian Ricci curvature and 2) a conservativeness principle about the semigroup generated by the Kohn-Rossi Laplacian. While some elementary notions of CR and pseudohermitian geometry are recalled, the terminology and advanced results in functional analysis used throughout the paper are not explained. Aside from a comment on renouncing to the naive generalization of the Bochner formula (which is known to be - unlike its Riemannian counterpart - difficult to deal with torsion terms) the author does not compare his version of the Bochner formula with the already existing ones in the mathematical literature (see \textit{A. Greenleaf} [Commun. Partial Differ. Equations 10, 191--217 (1985; Zbl 0563.58034)] and \textit{E. Barletta} [Tsukuba J. Math. 31, No. 1, 77--97 (2007; Zbl 1138.32020)]). Proofs are sketchy or missing.
scientific article; zbMATH DE number 5292752
scientific article