# Ricci-flat metrics on vector bundles over flag manifolds

## TL;DR

This paper constructs explicit complete Ricci-flat metrics on vector bundles over flag manifolds of SU(n), generalizing known metrics on conifolds and canonical bundles, expanding the class of explicit Ricci-flat geometries.

## Contribution

It provides new explicit Ricci-flat metrics on vector bundles over flag manifolds, extending previous constructions to a broader class of geometries.

## Key findings

- Explicit Ricci-flat metrics constructed
- Metrics generalize known conifold and canonical bundle metrics
- Applicable to all Kähler classes on the bundles

## 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 K\"ahler 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.