On the classification of weakly symmetric Finsler spaces (Q532574)

The first part of this paper is devoted to a general principle to classify non-Riemannian weakly symmetric Finsler spaces. Namely, if a connected manifold admits a weakly symmetric Finsler metric, then it admits also a weakly symmetric Riemannian metric. Rank one symmetric Riemannian manifolds are carefully studied and a complete list of weakly symmetric non-Riemannian Finsler spaces among these manifolds is obtained. Secondly, weakly symmetric Finsler metrics of Berwald type are analyzed and the author obtains a large class of reversible Finsler spaces with vanishing \(S\)-curvature.