On new explicit Riemannian SU(2(n+1))-holonomy metrics

TL;DR

This paper constructs explicit algebraic families of complete noncompact Ricci-flat metrics with special holonomy SU(2(n+1)), generalizing Calabi metrics to higher dimensions.

Contribution

It introduces new explicit algebraic formulas for Ricci-flat metrics with SU(2(n+1)) holonomy in higher dimensions, extending known Calabi metrics.

Findings

Explicit algebraic formulas for new Ricci-flat metrics

Metrics have holonomy SU(2(n+1))

Generalization of Calabi metrics to higher dimensions

Abstract

We construct in an explicit algebraic form a family of complete noncompact Ricci-flat metrics which generalize Calabi metrics in real dimension $4(n+1)$ and with holonomy $SU(2(n+1))$.