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 Carathéodory pseudo‐distance on CR manifolds.

中文翻译：

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伪Hermitian流形和Hermitian流形之间的广义全纯映象的Schwarz型引理

在本文中，我们考虑伪Hermitian流形和Hermitian流形之间的一些广义全纯映射。通过Bochner公式和比较定理，我们建立了相关的Schwarz型结果。作为推论，推导了基本CR函数的Liouville定理和小Picard定理。最后，我们研究了CR流形上的CRCarathéodory伪距离。