Schwarz type lemmas for pseudo-Hermitian manifolds

2019/09/06 by Dong, Yuxin, Ren, Yibin, Yu, Weike
#Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1909.02936

Abstract

In this paper, we consider some generalized holomorphic maps between pseudo-Hermitian manifolds. These maps include the CR maps and the transversally holomorphic maps. In terms of some sub-Laplacian or Hessian type Bochner formulas, and comparison theorems in the pseudo-Hermitian version, we are able to establish several Schwarz type results for both the CR maps and the transversally holomorphic maps between pseudo-Hermitian manifolds. Finally, we also discuss the CR hyperbolicity problem for pseudo-Hermitian manifolds.

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