Riemannian Geometry of Lie Algebroids

TL;DR

This paper extends Riemannian geometry to Lie algebroids, providing a generalized framework that retains classical tools and introduces new results on their integrability.

Contribution

It introduces Riemannian Lie algebroids as a new generalization and explores their classical and novel properties, especially integrability conditions.

Findings

Classical Riemannian tools are applicable to Lie algebroids.

New results on the integrability of Riemannian Lie algebroids.

Framework unifies geometric concepts across manifolds and Lie algebroids.

Abstract

We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting. We give also some new results on the integrability of Riemannian Lie algebroids.