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

In this article, we study the geodesic orbit Randers spaces of the form ( G / H , F ) {(G/H,F)} , such that G is one of the compact classical Lie groups SO ⁢ ( n ) {{\mathrm{S}}{\mathrm{O}}(n)} , SU ⁢ ( n ) {{\mathrm{S}}{\mathrm{U}}(n)} , Sp ⁢ ( n ) {{\mathrm{S}}{\mathrm{p}}(n)} , and H is a diagonally embedded product H 1 × ⋯ × H s {H_{1}\times\cdots\times H_{s}} , where H i {H_{i}} is of the same type as G. Such spaces include spheres, Stiefel manifolds, Grassmann manifolds, and flag manifolds. The present work is a contribution to the study of geodesic orbit Randers spaces ( G / H , F ) {(G/H,F)} with H semisimple. We construct new examples of non-Riemannian Randers g.o. metrics in homogeneous bundles over generalized Stiefel manifolds which are not naturally reductive. Also, we obtain the specific expressions of these Randers g.o. metrics.

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

Abstract: In this paper, we introduce the notion of standard homogeneous ( 𝛼 1 , 𝛼 2 ) metric, as a generalization for the normal homogeneity in Finsler geometry with relatively good computability. We explore the geodesic orbit (g.o. in short)

Cited by 3 publications

References 19 publications

Homogeneous Sub-Riemannian Manifolds Whose Normal Extremals are Orbits

Homogeneous Sub-Riemannian Manifolds Whose Normal Extremals are Orbits

The symmetric space, strong isotropy irreducibility and equigeodesic properties

Geodesic orbit Randers metrics in homogeneous bundles over generalized Stiefel manifolds

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