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arXiv · 1903.00044

Invariant Ricci-flat K\"ahler metrics on tangent bundles of compact symmetric spaces

P. M. Gadea·J. C. González-Dávila·I. V. Mykytyuk
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Abstract

We give a description of all $G$-invariant Ricci-flat K\"ahler metrics on the canonical complexification of any compact Riemannian symmetric space $G/K$ of arbitrary rank, by using some special local $(1,0)$ vector fields on $T(G/K)$. As the simplest application, we obtain the explicit description of the set of all complete $\mathrm{SO}(3)$-invariant Ricci-flat K\"ahler metrics on $T{\mathbb S}^2$, which includes the well-known Eguchi-Hanson-Stenzel metrics and a new one-parameter family of metrics.

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P. M. Gadea, J. C. González-Dávila, I. V. Mykytyuk. 2019-02-28. Invariant Ricci-flat K\"ahler metrics on tangent bundles of compact symmetric spaces. https://arxiv.org/abs/1903.00044

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