Invariant Kohn-Rossi cohomology and obstruction to embedding of compact real \((2n-1)\)-dimensional \(CR\) manifolds in \(\mathbb{C}^ N\)
type: Item
instance of: scholarly article
title: Invariant Kohn-Rossi cohomology and obstruction to embedding of compact real \((2n-1)\)-dimensional \(CR\) manifolds in \(\mathbb{C}^ N\)
zbMATH Open document ID: 0855.32011
published in: Journal of the Mathematical Society of Japan
publication date: 1996-07-29T00:00:00Z
review text: Let \(X\) be a compact \(CR\) manifold of dimension \(2n - 1\), \(n \geq 3\) and \((H,J)\) be the holomorphic tangent bundle of \(x\). A smooth \(S^1\)-action on \(X\) is said to be transversal holomorphic if it preserves \(H\) and commutes with \(J\), and the vector field which generates the action is transversal to \(H\) at all points of \(X\). Following Tanaka this action defines a differential operator \(N\) which acts on the Kohn-Rossi cohomology \(H^{p,q}_{KR} (X)\). Let \(\widetilde H^{p,q}_{K,R} (x)\) be the part on which \(N\) acts trivially. The authors prove the following Theorem: If \(X\) is strongly pseudoconvex and \(CR\)-embeddable in \(\mathbb{C}^N\) then \(\widetilde H^{p,q}_{KR} (X) = 0\) for all \(1 \leq p + q \leq 2n - N - 1\).
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 32T99
Mathematics Subject Classification ID: 32C35
zbMATH DE Number: 894113
zbMATH Keywords: embedding of compact real \((2n - 1)\)-dimensional \(CR\) manifolds
zbMATH Keywords: Kohn-Rossi cohomology
author: Hing Sun Luk
author: Stephen Yau
reviewed by: Giuseppe Tomassini
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/04810061
OpenAlex ID: W1997845171
DOI: 10.2969/JMSJ/04810061
description: scientific article; zbMATH DE number 894113