Open Access
March 2007 Proof of the projective Lichnerowicz-Obata conjecture
V. S. Matveev
J. Differential Geom. 75(3): 459-502 (March 2007). DOI: 10.4310/jdg/1175266281


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.


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V. S. Matveev. "Proof of the projective Lichnerowicz-Obata conjecture." J. Differential Geom. 75 (3) 459 - 502, March 2007.


Published: March 2007
First available in Project Euclid: 30 March 2007

zbMATH: 1115.53029
MathSciNet: MR2301453
Digital Object Identifier: 10.4310/jdg/1175266281

Rights: Copyright © 2007 Lehigh University

Vol.75 • No. 3 • March 2007
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