Geodesic orbit metrics in a class of homogeneous bundles over real and complex Stiefel manifolds
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2021
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910602146873344 |
|---|---|
| author | Arvanitoyeorgos, Andreas Souris, Nikolaos Panagiotis Statha, Marina |
| author_facet | Arvanitoyeorgos, Andreas Souris, Nikolaos Panagiotis Statha, Marina |
| contents | Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces $(M=G/H,g)$ 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 $(G/H,g)$, such that $G$ is one of the compact classical Lie groups $\SO(n)$, $U(n)$, and $H$ is a diagonally embedded product $H_1\times \cdots \times H_s$, where $H_j$ is of the same type as $G$. This class includes spheres, Stiefel manifolds, Grassmann manifolds and real flag manifolds. The present work is a contribution to the study of g.o. spaces $(G/H,g)$ with $H$ semisimple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_02908 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Geodesic orbit metrics in a class of homogeneous bundles over real and complex Stiefel manifolds Arvanitoyeorgos, Andreas Souris, Nikolaos Panagiotis Statha, Marina Differential Geometry 53C25, 53C30 Geodesic orbit spaces (or g.o. spaces) are defined as those homogeneous Riemannian spaces $(M=G/H,g)$ 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 $(G/H,g)$, such that $G$ is one of the compact classical Lie groups $\SO(n)$, $U(n)$, and $H$ is a diagonally embedded product $H_1\times \cdots \times H_s$, where $H_j$ is of the same type as $G$. This class includes spheres, Stiefel manifolds, Grassmann manifolds and real flag manifolds. The present work is a contribution to the study of g.o. spaces $(G/H,g)$ with $H$ semisimple. |
| title | Geodesic orbit metrics in a class of homogeneous bundles over real and complex Stiefel manifolds |
| topic | Differential Geometry 53C25, 53C30 |
| url | https://arxiv.org/abs/2103.02908 |