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This book is an exploration of Carnot-Carathéodory spaces through the perspective of Lie groups. It is intended to study these non-smooth geometries, focusing on the prototypical examples called Carnot groups. Carnot groups are a fundamental class of nilpotent Lie groups equipped with sub-Riemannian or, more generally, sub-Finsler structures. They play an essential role in various mathematical domains, including metric geometry and geometric group theory—as we shall see.

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Introduction

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  • 出版模式：

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  • 发表日期：

    2025年

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  • Enrico Le Donne

摘要

This book is an exploration of Carnot-Carathéodory spaces through the perspective of Lie groups. It is intended to study these non-smooth geometries, focusing on the prototypical examples called Carnot groups. Carnot groups are a fundamental class of nilpotent Lie groups equipped with sub-Riemannian or, more generally, sub-Finsler structures. They play an essential role in various mathematical domains, including metric geometry and geometric group theory—as we shall see.