Finsler metrics and the degree of symmetry of a closed manifold Shaoqiang Deng 22E4653C6058B20Minkowski representationsdegree of symmetryhomogeneous manifoldsFinsler metrics In this paper, we use the representation theory of compact Lie groups to prove that the degree of symmetry of a closed manifold can be realized by a non-Riemannian Finsler metric unless the manifold is diffeomorphic to a rank-one Riemannian symmetric space. As a by product, we obtain a sufficient and necessary condition for a coset space of a Lie group to admit invariant non-Riemannian Finsler metrics. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4198 10.1512/iumj.2011.60.4198 en Indiana Univ. Math. J. 60 (2011) 713 - 728 state-of-the-art mathematics http://iumj.org/access/