THE diameter estimate and its application to CR Obata's theorem on closed pseudohermitian (2n + 1)-manifolds
Journal
Transactions of the American Mathematical Society
Journal Volume
364
Journal Issue
7
Pages
3349-3363
Date Issued
2012
Author(s)
Wu, C.-T.
Abstract
In this paper, we obtain a sharp lower bound estimate for diameters with respect to an adapted metric in closed pseudohermitian $(2n+1)$-manifolds when a sharp lower bound estimate for the first positive eigenvalue of the sublaplacian is achieved. As a consequence, we confirm the CR Obata Conjecture on a closed pseudohermitian $(2n+1)$-manifold with an extra condition on covariant derivatives of torsion.
Type
journal article