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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.16450 |
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| _version_ | 1866909619802079232 |
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| author | Courtois, Gilles Lessa, Pablo Sequeira, Emiliano |
| author_facet | Courtois, Gilles Lessa, Pablo Sequeira, Emiliano |
| contents | We study the volume growth of horospheres in a Heintze group of the form R ___ A R d with A a diagonal derivation. We conclude that the isometry and quasi-isometry classes of horospheres (with their intrinsic geometry) coincide. Furthermore, if A is not a scalar multiple of the identity, then there are exactly two such classes, characterized by their volume growth, which we calculate explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16450 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Volume growth of horospheres in diagonalizable Heintze groups Courtois, Gilles Lessa, Pablo Sequeira, Emiliano Differential Geometry We study the volume growth of horospheres in a Heintze group of the form R ___ A R d with A a diagonal derivation. We conclude that the isometry and quasi-isometry classes of horospheres (with their intrinsic geometry) coincide. Furthermore, if A is not a scalar multiple of the identity, then there are exactly two such classes, characterized by their volume growth, which we calculate explicitly. |
| title | Volume growth of horospheres in diagonalizable Heintze groups |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2505.16450 |