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Ricci-flat metrics on the cone over CP^2 # \overline\CP^2

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Bykov,  Dmitri
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1712.07227.pdf
(Preprint), 851KB

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Citation

Bykov, D. (in preparation). Ricci-flat metrics on the cone over CP^2 # \overline\CP^2.


Cite as: https://hdl.handle.net/21.11116/0000-0000-BF23-2
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.