Totally geodesic submanifolds and polar actions on Stiefel manifolds
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929584453189632 |
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| author | Gorodski, Claudio Kollross, Andreas Rodríguez-Vázquez, Alberto |
| author_facet | Gorodski, Claudio Kollross, Andreas Rodríguez-Vázquez, Alberto |
| contents | We classify totally geodesic submanifolds of the real Stiefel manifolds of orthogonal two-frames. We also classify polar actions on these Stiefel manifolds, specifically, we prove that the orbits of polar actions are lifts of polar actions on the corresponding Grassmannian. In the case of cohomogeneity-one actions we are able to obtain a classification for all real, complex and quaternionic Stiefel manifolds of $k$-frames. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_08585 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Totally geodesic submanifolds and polar actions on Stiefel manifolds Gorodski, Claudio Kollross, Andreas Rodríguez-Vázquez, Alberto Differential Geometry Primary 53C30, Secondary 53C40, 57S15 We classify totally geodesic submanifolds of the real Stiefel manifolds of orthogonal two-frames. We also classify polar actions on these Stiefel manifolds, specifically, we prove that the orbits of polar actions are lifts of polar actions on the corresponding Grassmannian. In the case of cohomogeneity-one actions we are able to obtain a classification for all real, complex and quaternionic Stiefel manifolds of $k$-frames. |
| title | Totally geodesic submanifolds and polar actions on Stiefel manifolds |
| topic | Differential Geometry Primary 53C30, Secondary 53C40, 57S15 |
| url | https://arxiv.org/abs/2402.08585 |