Algebraic Constructions in the Category of Lie Algebroids

Details Algebraic Constructions in the Category of Lie Algebroids Algebraic Constructions in the Category of Lie Algebroids

2011-01-05

arxiv.org/abs/1101.0960v4

Mathematics

Differential Geometry

39 pages

Scientific paper

A generalized notion of a Lie algebroid is presented. Using this, the Lie algebroid generalized tangent bundle is obtained. A new point of view over (linear) connections theory on a ?ber bundle is presented. These connections are characterized by o horizontal distribution of the Lie algebroid generalized tangent bundle. Some basic properties of these generalized connections are investigated. Special attention to the class of linear connections is paid. The recently studied Lie algebroids connections can be recovered as special cases within this more general framework. In particular, all results are similar with the classical results. Formulas of Ricci and Bianchi type and linear connections of Levi-Civita type are presented.

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