Kaehler-Ricci solitons on homogeneous toric bundles (II)

Abstract

It is proved that an homogeneous toric bundles over a flag manifold G^/P admits a Kaehler-Ricci solitonic metric if and only if it is Fano. In particular, an homogeneous toric bundle of this kind is Kaehler-Einstein if and only if it is Fano and its Futaki invariant vanishes identically.