CONTACT 3-MANIFOLDS WITH THE REEB FLOW SYMMETRY

抄録

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 toSU(2) (or SO(3)), SL(2, $\boldsymbol{R}$) (or $O(1,2)$), the group $E(2)$ of rigid motions of Euclidean 2-plane with a contact left invariant Riemannian metric.