紧强伪凸CR流形间的Kohn-Rossi上同调及CR态射的不存在性

IF 1.3 1区数学 Q1 MATHEMATICS

Journal of Differential Geometry Pub Date : 2019-03-01 DOI:10.4310/JDG/1552442610

S. Yau, Huaiqing Zuo

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引用次数: 1

摘要

CR几何中的一个基本问题是：给定两个维数为2n−1的强伪凸CR流形X1和X2，它们之间是否存在非常CR态射？本文利用Kohn-Rosi上同调证明了这两个CR流形之间的非常CR态射的不存在性。特别地，如果对于1≤q≤n−2的任何（p，q），dimH-KR（X1）本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

One of the fundamental questions in CR geometry is: Given two strongly pseudoconvex CR manifolds X1 and X2 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 dimH KR(X1) < dimH p,q KR(X2) for any (p, q) with 1 ≤ q ≤ n− 2, then there is no non-constant CR morphism from X1 to X2.