Volume entropy of a family of rank one, split-solvable Lie groups of Abelian type
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914971708817408 |
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| author | Garcia-Lara, Rene |
| author_facet | Garcia-Lara, Rene |
| contents | We study a family of metrics on Euclidean space that generalize the left-invariant metric of the SOL group and the metric of the logarithmic model of Hyperbolic space. Suppose G is a connected, simply-connected, Heintze group of Abelian type with diagonalizable derivation or the horospherical product of two such groups. In this scenario, G is isometric to Euclidean space with a metric of the type considered. We have derived a formula for the volume entropy of metrics in this family and used it to solve a conjecture related to a family of 3-manifolds that interpolates between the SOL group and hyperbolic space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10631 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Volume entropy of a family of rank one, split-solvable Lie groups of Abelian type Garcia-Lara, Rene Differential Geometry Metric Geometry 58C35 (Primary) 51M25, 28A75 (Secondary) We study a family of metrics on Euclidean space that generalize the left-invariant metric of the SOL group and the metric of the logarithmic model of Hyperbolic space. Suppose G is a connected, simply-connected, Heintze group of Abelian type with diagonalizable derivation or the horospherical product of two such groups. In this scenario, G is isometric to Euclidean space with a metric of the type considered. We have derived a formula for the volume entropy of metrics in this family and used it to solve a conjecture related to a family of 3-manifolds that interpolates between the SOL group and hyperbolic space. |
| title | Volume entropy of a family of rank one, split-solvable Lie groups of Abelian type |
| topic | Differential Geometry Metric Geometry 58C35 (Primary) 51M25, 28A75 (Secondary) |
| url | https://arxiv.org/abs/2410.10631 |