2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/111440This is the first of a sequence of two papers. Here, a simple algebraic characterization of the Fano manifolds in the class of homogeneous toric bundles over a flag manifold G^C/P is provided in terms of symplectic data. The result of this paper is used in the second paper, where it is proved that an homogeneous toric bundle over a flag manifold admits a Kaehler-Ricci solitonic metric if and only if it is Fano.This is a new version of our previously posted paper "Homogeneous toric bundles with c_1(M)>0". The differences are mainly in the Abstract, Introdution and Title. This new version has been made necessary by the new results given in the next paper "Kaehler-Ricci solitons on homogeneous toric bundles (II)"Differential Geometry14M15; 32M12; 53C55text