Schwarz type lemmas for pseudo-Hermitian manifolds
Differential Geometry
2019-09-13 v1 Complex Variables
Abstract
In this paper, we consider some generalized holomorphic maps between pseudo-Hermitian manifolds. These maps include the \emph{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 \emph{CR} maps and the transversally holomorphic maps between pseudo-Hermitian manifolds. Finally, we also discuss the \emph{CR} hyperbolicity problem for pseudo-Hermitian manifolds.
Cite
@article{arxiv.1909.02936,
title = {Schwarz type lemmas for pseudo-Hermitian manifolds},
author = {Yuxin Dong and Yibin Ren and Weike Yu},
journal= {arXiv preprint arXiv:1909.02936},
year = {2019}
}
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