The Obata conjecture for dimension 2
The author confirms a conjecture of M. Obata on Riemannian surfaces (geometric sense) in the following form: Let \( (M^{2},g) \) be a connected compact two-dimensional Riemannian manifold. If the Lie group \( ({\mathbb{R}},+) \) acts on \( (M^{2},g) \) with projective transformations then the metric \( g \) is of constant positive curvature or all transformations are isometries. He announces the generalization of his result to the complete case. A projective transformation of a Riemannian manifold is a diffeomorphism taking geodesics to geodesics ignoring the parametrization.
scientific article; zbMATH DE number 2119264