Tangent Lie algebras to the holonomy group of a Finsler manifold (Q2904193)

The aim of this work is to find the largest Lie algebra of vector fields on the indicatrix such that all its elements are tangent to the holonomy group of a Finsler manifold. Two important notions are introduced towards this goal: the curvature algebra generated by curvature vector fields and the infinitesimal holonomy algebra generated by the smallest Lie algebra of vector fields on the indicatrix containing the curvature vector fields and their horizontal covariant derivative with respect to the Berwald connection. A main result is that this holonomy algebra is tangent to the holonomy group.