Invariant Ricci-flat Kähler metrics on tangent bundles of compact symmetric spaces

2019/02/28 by Gadea, P. M., González-Dávila, J. C., Mykytyuk, I. V.
#53C30 #53C35 #53C55 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.00044

Abstract

We give a description of all G-invariant Ricci-flat Kähler 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 SO(3)-invariant Ricci-flat Kähler metrics on T\mathbb S², which includes the well-known Eguchi-Hanson-Stenzel metrics and a new one-parameter family of metrics.

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