Four-dimensional Einstein metrics from biconformal deformations

Paul Baird; Jade Ventura

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arXiv · 2105.03653

Four-dimensional Einstein metrics from biconformal deformations

Paul Baird·Jade Ventura

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Abstract

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. One particular family of examples have ends that collapse asymptotically to ${\mathbb R}^2$.

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Paul Baird, Jade Ventura. 2021-05-08. Four-dimensional Einstein metrics from biconformal deformations. https://arxiv.org/abs/2105.03653

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