Geodesic orbit pseudo-Riemannian H-type nilmanifolds: case of minimal admissible Clifford modules
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908867573579776 |
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| author | Furutani, Kenro Markina, Irina Nikonorov, Yurii |
| author_facet | Furutani, Kenro Markina, Irina Nikonorov, Yurii |
| contents | We investigate the geodesic orbit property of pseudo-Riemannian nilmanifolds, specifically those known in the literature as pseudo $H$-type Lie groups -- i.e., 2-step nilpotent Lie groups of Heisenberg type equipped with a left invariant pseudo-Riemannian metric. The study of homogeneous geodesics on Riemannian $H$-type Lie groups was completed by C.~Riehm in 1984. In this work, we extend these results to the pseudo-Riemannian $H$-type Lie groups and provide a complete characterization of the geodesic orbit property for the case where the underlying Lie algebras are constructed from the admissible Clifford modules of minimal dimension. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_00470 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geodesic orbit pseudo-Riemannian H-type nilmanifolds: case of minimal admissible Clifford modules Furutani, Kenro Markina, Irina Nikonorov, Yurii Differential Geometry 53C30, 53C25, 22E25 We investigate the geodesic orbit property of pseudo-Riemannian nilmanifolds, specifically those known in the literature as pseudo $H$-type Lie groups -- i.e., 2-step nilpotent Lie groups of Heisenberg type equipped with a left invariant pseudo-Riemannian metric. The study of homogeneous geodesics on Riemannian $H$-type Lie groups was completed by C.~Riehm in 1984. In this work, we extend these results to the pseudo-Riemannian $H$-type Lie groups and provide a complete characterization of the geodesic orbit property for the case where the underlying Lie algebras are constructed from the admissible Clifford modules of minimal dimension. |
| title | Geodesic orbit pseudo-Riemannian H-type nilmanifolds: case of minimal admissible Clifford modules |
| topic | Differential Geometry 53C30, 53C25, 22E25 |
| url | https://arxiv.org/abs/2507.00470 |