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CR-analogue of the Siu- $ \partial\overline{\partial}$-formula and applications to the rigidity problem for pseudo-Hermitian harmonic maps


Authors: Song-Ying Li and Duong Ngoc Son
Journal: Proc. Amer. Math. Soc. 147 (2019), 5141-5151
MSC (2010): Primary 32Q05, 30Q15, 32V20
DOI: https://doi.org/10.1090/proc/12997
Published electronically: September 23, 2019
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Abstract: We give several versions of Siu's $ \partial \overline {\partial }$-formula for maps from a strictly pseudoconvex pseudo-Hermitian manifold $ (M^{2m+1}, \theta )$ into a Kähler manifold $ (N^n, g)$. We also define and study the notion of pseudo-Hermitian harmonicity for maps from $ M$ into $ N$. In particular, we prove a CR version of the Siu Rigidity Theorem for pseudo-Hermitian harmonic maps from a pseudo-Hermitian manifold with vanishing Webster torsion into a Kähler manifold having strongly negative curvature.


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Additional Information

Song-Ying Li
Affiliation: Department of Mathematics, University of California, Irvine, California 92697 — and — School of Mathematics and CS, Fujian Normal University, Fujian, People’s Republic of China
Email: sli@math.uci.edu

Duong Ngoc Son
Affiliation: Department of Mathematics, University of California, Irvine, California 92697
Email: snduong@math.uci.edu

DOI: https://doi.org/10.1090/proc/12997
Received by editor(s): May 22, 2015
Published electronically: September 23, 2019
Communicated by: Lei Ni
Article copyright: © Copyright 2019 American Mathematical Society