Standard homogeneous (α1,α2)${\big(\alpha _1,\alpha _2\big)}$‐metrics and geodesic orbit property

Abstract

AbstractIn this paper, we introduce the notion of standard homogeneous ‐metric, as a generalization for the normal homogeneity in Finsler geometry with relatively good computability. We explore the geodesic orbit (g.o. in short) property of this metric. Especially, when it is associated with a triple of compact Lie groups, we find new examples of g.o. Finsler spaces from H. Tamaru's classification list. Meanwhile, we prove that all standard g.o. ‐metrics on the Wallach spaces, , and , must be the normal homogeneous Riemannian metrics.