Kohn-Rossi cohomology and nonexistence of CR morphisms between compact strongly pseudoconvex CR manifolds
type: Item
instance of: scholarly article
title: Kohn-Rossi cohomology and nonexistence of CR morphisms between compact strongly pseudoconvex CR manifolds
zbMATH Open document ID: 1417.32037
author: Huaiqing Zuo
author: Stephen Yau
published in: Journal of Differential Geometry
publication date: 2019-03-15T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.jdg/1552442610
review text: One of the interesting questions in CR geometry is the existence of non-constant CR morphisms between strongly pseudo-convex CR manifolds of even dimensions. In this paper, and following their previous works, the authors consider this question. Their former results in this setting answer it in some considerable cases in particular in terms of the so-called plurigeneras of CR manifolds. However, there is no known method to compute these invariants just in terms of the known datum of CR manifolds. Accordingly, in this paper, the authors endeavor to classify the problem by means of the so-called Kohn-Rossi cohomology of CR manifolds. In particular, they show that for two strongly pseudo-convex CR manifolds $X_1$ and $X_2$ of dimension $2n-1$, if \[ \dim H^{p,q}_{KR}(X_1)< \dim H^{p,q}_{KR}(X_2) \] for any $(p,q)$ with $1\leq q\leq n-2$, then there is no non-constant CR morphism from $X_1$ to $X_2$.
reviewed by: Masoud Sabzevari
Mathematics Subject Classification ID: 32V15
Mathematics Subject Classification ID: 32T15
zbMATH DE Number: 7036516
zbMATH Keywords: strongly pseudoconvex CR manifolds
zbMATH Keywords: CR morphisms
zbMATH Keywords: Kohn-Rossi cohomology
MaRDI profile type: Publication
OpenAlex ID: W2921193166
Wikidata QID: Q115165291
DOI: 10.4310/JDG/1552442610
description: scientific article; zbMATH DE number 7036516