Ricci-Flat Metrics on Vector Bundles Over Flag Manifolds

Abstract

AbstractWe 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 $$\mathbb {CP}^1\times \mathbb {CP}^1$$CP1×CP1, as well as the metrics on canonical bundles over flag manifolds, recently constructed by van Coevering.