Address:
Laboratoire de Mathématiques de Bretagne Atlantique UMR 6205, Université de Brest, 6 av. Victor Le Gorgeu – CS 93837, 29238 Brest Cedex, France
Institute of Mathematics, University of the Philippines Diliman, C.P. Garcia Ave., 1101 Quezon City, Philippines
E-mail:
paul.baird@univ-brest.fr
jventura@math.upd.edu.ph
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. Examples of one particular family have ends which collapse asymptotically to $\mathbb{R}^2$.
AMSclassification: primary 53C25; secondary 53C18, 53C12.
Keywords: Einstein manifold, conformal foliation, semi-conformal map, biconformal deformation.
DOI: 10.5817/AM2021-5-255