Metrizable linear connections in a Lie algebroid

Abstract

A linear connection $D$ in a Lie algebroid is said to be metrizable if there exists a Riemannian metric $h$ in the Lie algebroid such that $Dh=0$. Conditions for the linear connection $D$ to be metrizable are investigated.Comment: p.10, no figures, Invited paper to celebrate Professor Constantin Udri\c{s}te, on the occasion of his seventie