Geodesic
Four-dimensional Einstein metrics from biconformal deformations
Archivum mathematicum, Tome 57 (2021) no. 5, pp. 255-283.

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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 $\mathbb{R}^2$.
DOI : 10.5817/AM2021-5-255
Classification : 53C12, 53C18, 53C25
Keywords: Einstein manifold; conformal foliation; semi-conformal map; biconformal deformation 
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Baird, Paul; Ventura, Jade. Four-dimensional Einstein metrics from biconformal deformations. Archivum mathematicum, Tome 57 (2021) no. 5, pp. 255-283. doi : 10.5817/AM2021-5-255. http://geodesic.mathdoc.fr/articles/10.5817/AM2021-5-255/

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