The Bochner-Type Formula and The First Eigenvalue of the sub-Laplacian on a Contact Riemannian Manifold
The Bochner-Type Formula and The First Eigenvalue of the sub-Laplacian on a Contact Riemannian Manifold
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DOI：
10.1016/j.difgeo.2014.10.002
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发表时间：
2014-12
期刊：
影响因子：
--
通讯作者：
Feifan Wu;Wei Wang
中科院分区：
文献类型：
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作者：
Feifan Wu;Wei Wang
接触黎曼流形不一定具有可积的复数结构，是 CR 几何中伪厄米流形的推广。这种流形上的田中-韦氏-丹野联系在伪埃尔米特情况中扮演了田中-韦氏联系的角色。我们证明了伪厄米博赫纳型公式的接触黎曼版本，并将关于亚拉普拉斯第一个非零特征值的锐下界的 CR Lichnerowicz 定理推广到接触黎曼情况。
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 Riemannian case.