Projective Lichnerowicz-Obata conjecture

Abstract

We solve two classical conjectures by showing that if an action of a connected Lie group 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.

38 pages, 1 figure

Cited by in corpus (2)

• Geodesically equivalent metrics in general relativity
• Two-dimensional metrics admitting precisely one projective vector field