Ricci-flat metrics on vector bundles over flag manifolds

Abstract

We construct explicit complete Ricci-flat metrics on the total spaces of certain vector bundles over flag manifolds of the group $SU(n)$, for all Kähler classes. These metrics are natural generalizations of the metrics of Candelas-de la Ossa on the conifold, Pando Zayas-Tseytlin on the canonical bundle over ${\mathbb{CP}}^1\times {\mathbb{CP}}^1$, as well as the metrics on canonical bundles over flag manifolds, recently constructed by van Coevering.

21 pages, 3 figures