%0 Journal Article %T Reflection quotients in Riemannian Geometry. A Geometric Converse to Chevalley's Theorem %A Robert Milson %J Mathematics %D 2001 %I arXiv %X Chevalley's theorem and it's converse, the Sheppard-Todd theorem, assert that finite reflection groups are distinguished by the fact that the ring of invariant polynomials is freely generated. We show that in the Euclidean case, a weaker condition suffices to characterize finite reflection groups, namely that a freely-generated polynomial subring is closed with respect to the gradient product. %U http://arxiv.org/abs/math/0111297v3