On the Obata theorem for the weighted Kohn Laplacian in a closed weighted Sasakian manifold

Chin-Tung Wu

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arXiv · 1912.10878

On the Obata theorem for the weighted Kohn Laplacian in a closed weighted Sasakian manifold

Chin-Tung Wu

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Abstract

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.

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BibTeX RIS

Chin-Tung Wu. 2019-12-23. On the Obata theorem for the weighted Kohn Laplacian in a closed weighted Sasakian manifold. https://arxiv.org/abs/1912.10878

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