Isospectral deformations of Eguchi-Hanson spaces a case study in noncompact noncommutative geometry

We study the isospectral deformations of the Eguchi-Hanson spaces along a torus isometric action in the noncompact noncommutative geometry. We concentrate on locality, smoothness and summability conditions of the nonunital spectral triples, and relate them to some geometric conditions to be noncommutative spin manifolds.