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}
}