Vanishing and conservativeness of harmonic forms of a non-compact CR manifold
type: Item
instance of: scholarly article
title: Vanishing and conservativeness of harmonic forms of a non-compact CR manifold
zbMATH Open document ID: 1164.32006
DOI: 10.4171/RLM/510
author: Jun Masamune
published in: Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni
publication date: 2008-06-25T00:00:00Z
review text: 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.
reviewed by: Sorin Dragomir
Mathematics Subject Classification ID: 32V20
Mathematics Subject Classification ID: 53C17
Mathematics Subject Classification ID: 58A14
zbMATH DE Number: 5292752
zbMATH Keywords: CR manifold
zbMATH Keywords: Sublaplacian
zbMATH Keywords: Kohn-Rossi laplacian
zbMATH Keywords: Essentially self-adjoint
zbMATH Keywords: Vanishing theorem
zbMATH Keywords: Conservative
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5292752