2014/07/14 by Ming Xu, Shaoqiang Deng, Xu, Ming +5 · 1 citation
Mathematics · #22E46 #53C30 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:22E46 #msc:53C30
paper · pdf · doi:10.48550/arxiv.1407.3582
The title is changed from 'Homogeneous Finsler spaces with positive flag curvature' to 'Even dimensional homogeneous Finsler spaces with positive flag curvature'. Add a flag curvature formula for homogeneous Finsler spaces and correct some typos
arxiv created 2015/03/29 · arxiv updated 2015/03/31
In this paper, we use the technique of Finslerian submersion to deduce a flag curvature formula for homogeneous Finsler spaces. Based on this formula, we give a complete classification of even-dimensional smooth coset spaces G/H admitting G-invariant Finsler metrics with positive flag curvature. It turns out that the classification list coincides with that of the even dimensional homogeneous Riemannian manifolds with positive sectional curvature obtained by N.R. Wallach. We also find out all the coset spaces admitting invariant non-Riemannian Finsler metrics with positive flag curvature.