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