Projective Lichnerowicz-Obata conjecture

Details Projective Lichnerowicz-Obata conjecture Projective Lichnerowicz-Obata conjecture

2004-07-20

arxiv.org/abs/math/0407337v1

J. of Differential Geometry, 75(2007), 459-502

Mathematics

Differential Geometry

38 pages, 1 figure

Scientific paper

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.

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