In this paper,we briefly survey the classification of positively curved homogeneous Finsler manifolds.We propose a new method in the even dimensional case,which proves that an even dimensional smooth coset space admits positively curved homogeneous Finsler metrics if and only if it admits positively curved homogeneous Riemannian metrics.
关键词
旗曲率/齐性Finsler空间/不变Finsler度量/正曲率Finsler流形
Key words
flag curvature/homogeneous Finsler space/invariant Finsler metric/positively curved Finsler manifold
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