The diameter estimate and its application to CR Obata’s Theorem on closed pseudohermitian (2𝑛+1)-manifolds

Chang, Shu-Cheng; Wu, Chin-Tung

doi:10.1090/S0002-9947-2012-05620-0

The diameter estimate and its application to CR Obata’s Theorem on closed pseudohermitian $(2n+1)$-manifolds
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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.

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