Models of Finsler Geometry on Lie algebroids

Abstract

Horizontal endomorphisms, almost complex structures, vertical, horizontal and complete lifts on prolongation of a Lie algebroid are considered. Then using exact sequences, semisprays are constructed. Moreover, important geometrical objects such as classical distinguished connections, torsions and partial curvatures are studied on prolongation of Lie algebroids. Considering pullback bundle, covariant derivatives are scrutinized based on anchor map. Several Finsler geometry models on Lie algebroid structures, will organized via recent arguments. Finally, it will be overhaulled some special Finsler Lie algebroid spaces.

arXiv admin note: text overlap with arXiv:math/0407528, arXiv:1211.4561 by other authors

Cited by in corpus (4)

• Symmetries of second order differential equations on Lie algebroids
• Weyl's Theory in the Generalized Lie Algebroids Framework
• Connections in holomorphic Lie algebroids
• Curvature collineations on Lie algebroid structure