Abstract
We prove that if a connected Lie group action on a complete Riemannian manifold preserves the geodesics (considered as unparameterized curves), then the metric has constant positive sectional curvature, or the group acts by affine transformations.
Citation
V. S. Matveev. "Proof of the projective Lichnerowicz-Obata conjecture." J. Differential Geom. 75 (3) 459 - 502, March 2007. https://doi.org/10.4310/jdg/1175266281
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