English

On the Obata Theorem in a weighted Sasakian manifold

Differential Geometry 2019-07-31 v1

Abstract

In this paper, we generalize the CR Obata theorem to a compact strictly pseudoconvex CR manifold with a weighted volume measure. More precisely, we first derive the weighted CR Reilly's formula associated with the Witten sub-Laplacian and obtain the corresponding first eigenvalue estimate. With its applications, we obtain the CR Obata theorem in a compact weighted Sasakian manifold with or without boundary.

Keywords

Cite

@article{arxiv.1907.12800,
  title  = {On the Obata Theorem in a weighted Sasakian manifold},
  author = {Shu-Cheng Chang and Daguang Chen and Chin-Tung Wu},
  journal= {arXiv preprint arXiv:1907.12800},
  year   = {2019}
}