Certain contact metrics satisfying the Miao–Tam critical condition
Volume 116 / 2016
Annales Polonici Mathematici 116 (2016), 263-271
MSC: Primary 53C25, 53C21; Secondary 53D15.
DOI: 10.4064/ap3704-11-2015
Published online: 18 April 2016
Abstract
We study certain contact metrics satisfying the Miao–Tam critical condition. First, we prove that a complete $K$-contact metric satisfying the Miao–Tam critical condition is isometric to the unit sphere $S^{2n+1}$. Next, we study $(\kappa , \mu )$-contact metrics satisfying the Miao–Tam critical condition.
