English

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 CP2#CP2\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.

Keywords

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