Journal of Differential Geometry

Nonconstant CR morphisms betweenc compact strongly pseudoconvex CR manifolds and étale covering between resolutions of isolated singularities

Yu-Chao Tu, Stephen S.-T. Yau, and Huaiqing Zuo

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Abstract

Strongly pseudoconvex CR manifolds are boundaries of Stein varieties with isolated normal singularities. We prove that any non- constant CR morphism between two $(2n−1)$-dimensional strongly pseudoconvex CR manifolds lying in an $n$-dimensional Stein variety with isolated singularities are necessarily a CR biholomorphism. As a corollary, we prove that any nonconstant self map of $(2n − 1)$-dimensional strongly pseudoconvex CR manifold is a CR automorphism. We also prove that a finite étale covering map between two resolutions of isolated normal singularities must be an isomorphism.

Article information

Source
J. Differential Geom., Volume 95, Number 2 (2013), 337-354.

Dates
First available in Project Euclid: 9 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1376053450

Digital Object Identifier
doi:10.4310/jdg/1376053450

Mathematical Reviews number (MathSciNet)
MR3128987

Zentralblatt MATH identifier
1277.32036

Citation

Tu, Yu-Chao; Yau, Stephen S.-T.; Zuo, Huaiqing. Nonconstant CR morphisms betweenc compact strongly pseudoconvex CR manifolds and étale covering between resolutions of isolated singularities. J. Differential Geom. 95 (2013), no. 2, 337--354. doi:10.4310/jdg/1376053450. https://projecteuclid.org/euclid.jdg/1376053450


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