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

Lei Zhang and Ming Xu

Mathematische Nachrichten, 2022, vol. 295, issue 7, 1443-1453

Abstract: In this paper, we introduce the notion of standard homogeneous (α1,α2)$\big (\alpha _1,\alpha _2\big )$‐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. (α1,α2)$\big (\alpha _1,\alpha _2\big )$‐metrics on the Wallach spaces, W6=SU(3)/T2$W^6=SU(3)/T^2$, W12=Sp(3)/Sp(1)3$W^{12}=Sp(3)/Sp(1)^3$ and W24=F4/Spin(8)$W^{24}=F_4/Spin(8)$, must be the normal homogeneous Riemannian metrics.

Date: 2022
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