Curvature collineations on Lie algebroid structure

TL;DR

This paper explores how Lie symmetries of sprays on Lie algebroids serve as curvature collineations for certain classical tensors, linking symmetry properties to geometric invariants.

Contribution

It establishes that Lie symmetries of sprays on Lie algebroids act as curvature collineations for classical tensors, revealing new geometric relationships.

Findings

Lie symmetries are curvature collineations for classical tensors

Prolongation of Lie algebroids with sprays reveals symmetry-invariant properties

New connections between Lie symmetries and geometric tensors in Lie algebroids

Abstract

Considering prolongation of a Lie algebroid equipped with a spray, defining some classical tensors, we show that a Lie symmetry of a spray is a curvature collineation for these tensors.