Rough similarity of left-invariant Riemannian metrics on some Lie groups

Enrico Le Donne; Gabriel Pallier; Xiangdong Xie

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arXiv · 2208.06510

Rough similarity of left-invariant Riemannian metrics on some Lie groups

Enrico Le Donne·Gabriel Pallier·Xiangdong Xie

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Abstract

We consider Lie groups that are either Heintze groups or Sol-type groups, which generalize the three-dimensional Lie group SOL. We prove that all left-invariant Riemannian metrics on each such a Lie group are roughly similar via the identity. This allows us to reformulate in a common framework former results by Le Donne-Xie, Eskin-Fisher-Whyte, Carrasco Piaggio, and recent results of Ferragut and Kleiner-M\"uller-Xie, on quasiisometries of these solvable groups.

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BibTeX RIS

Enrico Le Donne, Gabriel Pallier, Xiangdong Xie. 2022-08-12. Rough similarity of left-invariant Riemannian metrics on some Lie groups. https://arxiv.org/abs/2208.06510

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