AN OBATA-TYPE THEOREM IN CR GEOMETRY

作者：Li, Song-Ying^*; Wang, Xiaodong

来源：Journal of Differential Geometry, 2013, 95(3): 483-502.

• MANIFOLD
• EIGENVALUE

We discuss a sharp lower bound for the first positive eigenvalue of the sublaplacian on a closed, strictly pseudoconvex pseudohermitian manifold of dimension 2m + 1 >= 5 . We prove that the equality holds iff the manifold is equivalent to the CR sphere up to a scaling. For this purpose, we establish an Obata-type theorem in CR geometry that characterizes the CR sphere in terms of a nonzero function satisfying a certain overdetermined system. Similar results are proved in dimension 3 under an additional condition.

• 出版日期2013-11
• 单位福建师范大学