Abstract
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 $\mathrm{SU}(2)$ (or $\mathrm{SO}(3)$), $\mathrm{SL}(2,\boldsymbol{R})$ (or $O(1,2)$), the group $E(2)$ of rigid motions of Euclidean 2-plane with a contact left invariant Riemannian metric.
Citation
Jong Taek Cho. "Contact 3-manifolds with the Reeb-flow symmetry." Tohoku Math. J. (2) 66 (4) 491 - 500, 2014. https://doi.org/10.2748/tmj/1432229193
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