## CR-analogue of the Siu-$$\partial \overline{\partial}$$-formula and applications to the rigidity problem for pseudo-Hermitian harmonic maps.(English)Zbl 1429.32037

Summary: 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.

### MSC:

 32Q05 Negative curvature complex manifolds 32Q15 Kähler manifolds 32V20 Analysis on CR manifolds
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### References:

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