Geometric objects defined by almost Lie structures
Volume 54 / 2001
Banach Center Publications 54 (2001), 217-233
MSC: 53B15, 55R10, 55R25, 53C07, 22A30.
DOI: 10.4064/bc54-0-12
Abstract
The aim of this paper is to extend from manifolds to vector bundles some classical geometric objects, associated with Lagrange and Hamilton metrics. Considering vector bundles endowed with almost Lie structures, defined in \cite{P2} by one of the authors, some geometric objects like R-(semi)sprays and R-connections of Cartan type are defined and studied. It is proved that the Lagrange equations deduced for Lie algebroids by A. Weinstein have a similar form for almost Lie structures.
