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
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10.1512/iumj.2011.60.4198
10.1512/iumj.2011.60.4198
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Indiana Univ. Math. J. 60 (2011) 713 - 728
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