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arXiv · 1109.1242

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

Constantin M. Arcuş
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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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Constantin M. Arcuş. 2013-08-14. Metrizability of the Lie algebroid generalized tangent bundle and (generalized) Lagrange $(ρ,η)$-spaces. https://arxiv.org/abs/1109.1242

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