CONTACT 3-MANIFOLDS WITH THE REEB FLOW SYMMETRY

摘要

We prove that the Ricci operator on a contact Riemannian 3-manifold M is invariant along the Reeb flow if and only if M is Sasakian or locally isometric to SU(2) (or SO(3)), SL(2, R) (or O(1, 2)), the group E(2) of rigid motions of Euclidean 2-plane with a contact left invariant Riemannian metric.