Ricci-flat metrics on the cone over ${\mathbb{CP}}^2\#\overline{{\mathbb{CP}}^2}$

Abstract

We describe a framework for constructing the Ricci-flat metrics on the total space of the canonical bundle over ${\mathbb{CP}}^2\#\overline{{\mathbb{CP}}^2}$ (the del Pezzo surface of rank one). We construct explicitly the first-order deformation of the so-called `orthotoric metric' on this manifold. We also show that the deformation of the corresponding conformal Killing-Yano form does not exist.

56 pages, 4 figures

References in corpus (1)

• Cohomogeneity one Einstein-Sasaki 5-manifolds