Metrizability of the Lie algebroid generalized tangent bundle and (generalized) Lagrange (ρ,η)-spaces

2011/09/06 by Constantin M. Arcuş, Arcuş, Constantin M. · 1 citation
Mathematics · #53C05 #53C07 #53C60 #58B20 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:53C05 #msc:53C07 #msc:53C60 #msc:58B20

paper · pdf · doi:10.48550/arxiv.1109.1242

33 pages

arxiv created 2013/08/14 · arxiv updated 2013/08/15

Abstract

A class of metrizable vector bundles in the general framework of generalized Lie algebroids have been presented in the eight reference. Using a generalized Lie algebroid we obtain the Lie algebroid generalized tangent bundle of a vector bundle. This Lie algebroid is a new example of metrizable vector bundle. A new class of Lagrange spaces, called by use, generalized Lagrange (ρ?;η?)-space, Lagrange (ρ?;η?)-space and Finsler (ρ?;η?)-space are presented. In the particular case of Lie algebroids, new and important results are presented. In particular, if all morphisms are identities morphisms, then the classical results are obtained.

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• Mechanical Systems in the Generalized Lie Algebroids Framework

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