Foliations of hyperbolic space by constant mean curvature surfaces sharing ideal boundary.
Foliations on closed geodesics with positive mixed sectional curvature and special behaviour of -Jacobi fields.
Foliations with complex leaves
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 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 -manifolds. Examples of one particular family have ends which collapse asymptotically...