Four-dimensional Einstein metrics from biconformal deformations

Biconformal deformations take place in the presence of a conformal foliation, deforming by different factors tangent to and orthogonal foliation. Four-manifolds endowed with foliation surfaces present natural context put into effect this process. We develop tools calculate transformation Ricci curvature under such apply our method construct Einstein $4$-manifolds. One particular family examples have ends that collapse asymptotically ${\mathbb R}^2$.