Vol. 316, No. 1, 2022

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Rigidity of CR morphisms

Xiankui Meng and Stephen Shing-Toung Yau

Vol. 316 (2022), No. 1, 207–216
Abstract

Let X1 and X2 be two compact strongly pseudoconvex CR manifolds of dimension 2n 1 5 which are boundaries of complex varieties V 1 and V 2 with only isolated normal singularities in N1 and N2, respectively. We show that any nonconstant CR morphism from X1 to X2 can be extended to a finite holomorphic covering map from V 1 to V 2 in the case where V 2 has only isolated complete intersection singularities. In particular, there is no nonconstant CR morphism between the links of two isolated complete intersection singularities with different embedding codimensions. Finally, using Kohn–Rossi cohomology, we obtain some sufficient conditions for the nonexistence of CR morphisms from X1 to X2.

Dedicate to Professor H. Blaine Lawson on the occasion of his 80th birthday

Keywords
strongly pseudoconvex CR manifold, rigidity of CR morphism, isolated complete intersection singularity, Kohn–Rossi cohomology
Mathematical Subject Classification
Primary: 32S20, 32V99
Milestones
Received: 20 June 2021
Revised: 6 October 2021
Accepted: 5 November 2021
Published: 26 February 2022
Authors
Xiankui Meng
School of Sciences
Beijing University of Posts and Telecommunications
Beijing
China
Stephen Shing-Toung Yau
Department of Mathematical Sciences
Tsinghua University
Beijing
China