Berwald-type and Yano-type connections on Lie algebroids

Abstract

In a new approach, by using the exact sequences, semisprays on the prolongation of a Lie algebroids are introduced and many important results on the semisprays and sprays are obtained. Also, the horizontal endomorphisms, almost complex structures, vertical, horizontal and complete lifts on the prolongation of a Lie algebroid are considered. Then the distinguished connections on the prolongation of a Lie algebroid are introduced and the torsion and curvature tensors of these connections are considered. In particular, the Berwald-type and Yano-type connections are studied.