Actions de \({\mathbb{R}}\) et courbure de Ricci du fibré unitaire tangent des surfaces. (Actions of \({\mathbb{R}}\) and Ricci curvature on tangent circle bundles of surfaces) (Q1822365)

We give a characterization of 2-dimensional Riemannian manifolds (M,g) (in particular, of surfaces with constant Gaussian curvature \(K=1/c^ 2\), 0, \(-1/c^ 2\), respectively) whose tangent circle bundle \((T_ cM,g^ s)\) \((g^ s=Sasaki\) metric) admit an ''almost regular'' vector field belonging to an eigenspace of the Ricci operator.