CR-analogue of the Siu-$\partial \overline {\partial }$-formula and applications to the rigidity problem for pseudo-Hermitian harmonic maps
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- by Song-Ying Li and Duong Ngoc Son PDF
- Proc. Amer. Math. Soc. 147 (2019), 5141-5151 Request permission
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.References
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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
- MR Author ID: 228844
- Email: sli@math.uci.edu
- Duong Ngoc Son
- Affiliation: Department of Mathematics, University of California, Irvine, California 92697
- MR Author ID: 800658
- Email: snduong@math.uci.edu
- Received by editor(s): May 22, 2015
- Published electronically: September 23, 2019
- Communicated by: Lei Ni
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 5141-5151
- MSC (2010): Primary 32Q05, 30Q15, 32V20
- DOI: https://doi.org/10.1090/proc/12997
- MathSciNet review: 4021076