Schwarz-type lemmas for generalized holomorphic maps between pseudo-Hermitian manifolds and Hermitian manifolds

摘要

In this paper, we consider some generalized holomorphic maps between pseudo-Hermitian manifolds and Hermitian manifolds. By Bochner formulas and comparison theorems, we establish related Schwarz-type results. As corollaries, the Liouville theorem and little Picard theorem for basic CR functions are deduced. Finally, we study CR Caratheodory pseudo-distance on CR manifolds.