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arXiv · 2410.10631

Volume entropy of a family of rank one, split-solvable Lie groups of Abelian type

Rene Garcia-Lara
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Abstract

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.

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Rene Garcia-Lara. 2024-10-14. Volume entropy of a family of rank one, split-solvable Lie groups of Abelian type. https://arxiv.org/abs/2410.10631

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