CR-Analogue of Siu-$\partial \bar{\partial }$-formula and Applications to Rigidity problem for pseudo-Hermitian harmonic maps

Abstract

We give several versions of Siu's $\partial \bar{\partial }$-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 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.

10 pages, to appear in Proc. Amer. Math. Soc

Cited by in corpus (1)

• Semi-isometric CR immersions of CR manifolds into Kähler manifolds and applications