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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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