On the sub-Riemannian geometry of the quaternionic Heisenberg group
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911401200582656 |
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| author | Kim, Joonhyung Platis, Ioannis D. Sun, Li-Jie |
| author_facet | Kim, Joonhyung Platis, Ioannis D. Sun, Li-Jie |
| contents | Utilizing the framework of quaternionic contact geometry, we define a sequence of Riemannian metrics $\{g_L\}$ on the quaternionic Heisenberg group $\mathfrak{H}_{\mathbb{H}}$ by rescaling the vertical directions. By analyzing the limit of this sequence, we characterize the Carnot-Carathéodory geodesics and provide the explicit description of the Carnot-Carathéodory distance and spheres in $\mathfrak{H}_{\mathbb{H}}$ . Furthermore, we derive a general formula for the horizontal mean curvature of hypersurfaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_11312 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the sub-Riemannian geometry of the quaternionic Heisenberg group Kim, Joonhyung Platis, Ioannis D. Sun, Li-Jie Differential Geometry Primary 53C17, Secondary 53C42, 53C26 Utilizing the framework of quaternionic contact geometry, we define a sequence of Riemannian metrics $\{g_L\}$ on the quaternionic Heisenberg group $\mathfrak{H}_{\mathbb{H}}$ by rescaling the vertical directions. By analyzing the limit of this sequence, we characterize the Carnot-Carathéodory geodesics and provide the explicit description of the Carnot-Carathéodory distance and spheres in $\mathfrak{H}_{\mathbb{H}}$ . Furthermore, we derive a general formula for the horizontal mean curvature of hypersurfaces. |
| title | On the sub-Riemannian geometry of the quaternionic Heisenberg group |
| topic | Differential Geometry Primary 53C17, Secondary 53C42, 53C26 |
| url | https://arxiv.org/abs/2601.11312 |