Riemannian geometry of 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.

Keywords

• Lie algebroids
• Lie groupoids
• Riemannian metrics