The metrizability of the generalized tangent bundle of dual of a vector bundle

TL;DR

This paper introduces the metrizability of the generalized tangent bundle of the dual of a vector bundle, expanding the class of metrizable vector bundles with new structures and applications in Hamilton spaces.

Contribution

It presents the Lie algebroid generalized tangent bundle of a dual vector bundle as a new example of a metrizable vector bundle and introduces new classes of Hamilton spaces.

Findings

Lie algebroid generalized tangent bundle is metrizable

New classes of Hamilton ( ho, ext{eta})-spaces are defined

Classical results are recovered when morphisms are identities

Abstract

Two new classes of metrizable vector bundles have been presented in the papers [1] and [4]. The Lie algebroid generalized tangent bundle of a dual vector bundle is presented. This Lie algebroid is a new example of metrizable vector bundle. A new class of Hamilton spaces, called by use, generalized Hamilton (\rho,\eta)-space, Hamilton (\rho,\eta)-space and Cartan (\rho,\eta)-space are presented. The results obtained in the particular case of Lie algebroids emphasize the importance and the utility of our new method by work. In particular, if all morphisms are identities morphisms, then the classical results are obtained.