Ricci-flat metrics on the cone over $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$
High Energy Physics - Theory
2017-12-21 v1 General Relativity and Quantum Cosmology
Differential Geometry
Abstract
We describe a framework for constructing the Ricci-flat metrics on the total space of the canonical bundle over (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.
Cite
@article{arxiv.1712.07227,
title = {Ricci-flat metrics on the cone over $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$},
author = {Dmitri Bykov},
journal= {arXiv preprint arXiv:1712.07227},
year = {2017}
}
Comments
56 pages, 4 figures