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arXiv · 1501.06775

The Bochner-Type Formula and The First Eigenvalue of the sub-Laplacian on a Contact Riemannian Manifold

Feifan Wu·Wei Wang
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Abstract

Contact Riemannian manifolds, with not necessarily integrable complex structures, are the generalization of pseudohermitian manifolds in CR geometry. The Tanaka-Webster-Tanno connection on such a manifold plays the role of Tanaka-Webster connection in the pseudohermitian case. We prove the contact Riemannian version of the pseudohermitian Bochner-type formula, and generalize the CR Lichnerowicz theorem about the sharp lower bound for the first nonzero eigenvalue of the sub-Laplacian to the contact Riemannnian case.

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Feifan Wu, Wei Wang. 2015-01-27. The Bochner-Type Formula and The First Eigenvalue of the sub-Laplacian on a Contact Riemannian Manifold. https://arxiv.org/abs/1501.06775

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