English

A generalization of the Schwarz lemma for transversally harmonic maps

Differential Geometry 2022-05-25 v1

Abstract

In this paper, we consider transversally harmonic maps between Riemannian manifolds with Riemannian foliations. In terms of the Bochner techniques and sub-Laplacian comparison theorem, we are able to establish a generalization of the Schwarz lemma for transversally harmonic maps of bounded generalized transversal dilatation. In addition, we also obtain a Schwarz type lemma for transversally holomorphic maps between K\"ahler foliations.

Keywords

Cite

@article{arxiv.2205.11774,
  title  = {A generalization of the Schwarz lemma for transversally harmonic maps},
  author = {Xin Huang and Weike Yu},
  journal= {arXiv preprint arXiv:2205.11774},
  year   = {2022}
}