The Lichnerowicz-Obata Theorem on Sub-Riemannian Manifolds with Transverse Symmetries

被引：10

作者：

Baudoin, Fabrice ^{[1
]}

Kim, Bumsik ^{[1
]}

机构：

[1] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2016年 / 26卷 / 01期

关键词：

Sub-Riemannian geometry; Obata theorem; Lichnerowicz estimate; QUATERNIONIC CONTACT MANIFOLD; SUBELLIPTIC HEAT KERNEL; 1ST EIGENVALUE; LAPLACIAN; INEQUALITIES; BOUNDS;

D O I：

10.1007/s12220-014-9542-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a lower bound for the first eigenvalue of the sub-Laplacian on sub-Riemannian manifolds with transverse symmetries. When the manifold is of H-type, we obtain a corresponding rigidity result: If the optimal lower bound for the first eigenvalue is reached, then the manifold is equivalent to a 1- or a 3-Sasakian sphere.

引用

页码：156 / 170

页数：15

共 23 条

[1]

[Anonymous], 2006, Progress in Mathematics

[2]

Aribi A., J GEOM ANAL IN PRESS

[3] THE LICHNEROWICZ THEOREM ON CR MANIFOLDS [J].