## Journal of Differential Geometry

### Kohn–Rossi cohomology and nonexistence of CR morphisms between compact strongly pseudoconvex CR manifolds

#### 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 $X_2$.

#### Article information

Source
J. Differential Geom., Volume 111, Number 3 (2019), 567-580.

Dates
First available in Project Euclid: 13 March 2019

https://projecteuclid.org/euclid.jdg/1552442610

Digital Object Identifier
doi:10.4310/jdg/1552442610

Mathematical Reviews number (MathSciNet)
MR3934600

Zentralblatt MATH identifier
07036516

#### Citation

Yau, Stephen S.-T.; Zuo, Huaiqing. Kohn–Rossi cohomology and nonexistence of CR morphisms between compact strongly pseudoconvex CR manifolds. J. Differential Geom. 111 (2019), no. 3, 567--580. doi:10.4310/jdg/1552442610. https://projecteuclid.org/euclid.jdg/1552442610