Projective Lichnerowicz-Obata conjecture
Differential Geometry
2011-08-08 v1 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.math/0407337,
title = {Projective Lichnerowicz-Obata conjecture},
author = {Vladimir S. Matveev},
journal= {arXiv preprint arXiv:math/0407337},
year = {2011}
}
Comments
38 pages, 1 figure