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

Autor:	Garcia-Lara, Rene
Rok vydání:	2024
Předmět:	Mathematics - Differential Geometry Mathematics - Metric Geometry 58C35 (Primary) 51M25 28A75 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 19 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.10631 Zobrazit plný text záznamu View this record from Arxiv