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March 2019 Kohn–Rossi cohomology and nonexistence of CR morphisms between compact strongly pseudoconvex CR manifolds
Stephen S.-T. Yau, Huaiqing Zuo
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J. Differential Geom. 111(3): 567-580 (March 2019). DOI: 10.4310/jdg/1552442610

Abstract

One of the fundamental questions in CR geometry is: Given two strongly pseudoconvex CR manifolds $X_1$ and $X_2$ of dimension $2n-1$, is there a non-constant CR morphism between them? In this paper, we use Kohn–Rossi cohomology to show the non-existence of non-constant CR morphism between such two CR manifolds. Specifically, if $\dim H^{p,q}_{KR} (X_1) \lt \dim H^{p,q}_{KR} (X_2)$ for any $(p, q)$ with $1 \leq q \leq n-2$, then there is no non-constant CR morphism from $X_1$ to $X_2$.

Dedication

Dedicated to Professor H. Blaine Lawson, Jr. on the occasion of his 75th birthday.

Citation

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Stephen S.-T. Yau. Huaiqing Zuo. "Kohn–Rossi cohomology and nonexistence of CR morphisms between compact strongly pseudoconvex CR manifolds." J. Differential Geom. 111 (3) 567 - 580, March 2019. https://doi.org/10.4310/jdg/1552442610

Information

Received: 5 February 2016; Published: March 2019
First available in Project Euclid: 13 March 2019

zbMATH: 07036516
MathSciNet: MR3934600
Digital Object Identifier: 10.4310/jdg/1552442610

Rights: Copyright © 2019 Lehigh University

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Vol.111 • No. 3 • March 2019
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