On the Obata theorem for the weighted Kohn Laplacian in a closed weighted Sasakian manifold
- Resource Type
- Working Paper
- Authors
- Wu, Chin-Tung
- Source
- Subject
- Mathematics - Differential Geometry
Primary 32V05, 32V20, Secondary 53C56
- Language
In this paper, we generalize the CR Obata theorem for the Kohn Laplacian to a closed strictly pseudoconvex CR manifold with a weighted volume measure. More precisely, we first derive the weighted CR Reilly's formula associated with the weighted Kohn Laplacian and obtain the corresponding first eigenvalue estimate. With its application, we obtain the CR Obata theorem in a closed weighted Sasakian manifold.
Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:1907.12800