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Geodesic orbit metrics in a class of homogeneous bundles over quaternionic Stiefel manifolds
Journal of Geometry and Physics ( IF 1.6 ) Pub Date : 2021-03-22 , DOI: 10.1016/j.geomphys.2021.104223
Andreas Arvanitoyeorgos , Nikolaos Panagiotis Souris , Marina Statha

Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces (M=GH,g) whose geodesics are orbits of one-parameter subgroups of G. The corresponding metric g is called a geodesic orbit metric. We study the geodesic orbit spaces of the form (Sp(n)Sp(n1)××Sp(ns),g), with 0<n1++nsn. Such spaces include spheres, quaternionic Stiefel manifolds, Grassmann manifolds and quaternionic flag manifolds. The present work is a contribution to the study of g.o. spaces (GH,g) with H semisimple.



中文翻译:

四阶Stiefel流形上一类同质束中的测地轨道度量。

测地线轨道空间(或走行空间)定义为齐次黎曼空间 中号=GHG 其测地线是的一参数子群的轨道 G。相应的指标G被称为测地轨道度量。我们研究形式的测地轨道空间SPñSPñ1个××SPñsG, 和 0<ñ1个++ñsñ。这样的空间包括球体,四元Stiefel流形,Grassmann流形和四元旗形流形。目前的工作对围棋空间的研究做出了贡献GHGH 半简单的。

更新日期:2021-04-04
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