Sub-Riemannian geometry and Lie groups. Part II. Curvature of metric spaces, coadjoint orbits and associated representations

TL;DR

This paper explores the curvature of metric spaces, coadjoint orbits, and related representations within the context of sub-Riemannian geometry on Lie groups, extending foundational theories in geometric analysis.

Contribution

It advances the understanding of curvature in sub-Riemannian spaces and its relation to Lie group representations, building on previous foundational work in the series.

Findings

Analysis of curvature properties in sub-Riemannian metric spaces

Connections between coadjoint orbits and geometric structures

Implications for representation theory of Lie groups

Abstract

This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at http://arxiv.org/abs/math.MG/0210189, and "Tangent bundles to sub-Riemannian groups", math.MG/0307342, available at http://arxiv.org/abs/math.MG/0307342 .