Benoît Daniel, from the University of Lorraine, will give the geometry seminar on 20th October, at 2pm in O8.08, 8th floor of building NO. His title is Minimal isometric immersions into $latex S^2 \times \mathbf{R}$ and $latex H^2 \times \mathbf{R}$. His abstract follows.
A classical result in submanifold theory is that any simply connected minimal surface in Euclidean space R^3 belongs to a one-parameter family of minimal surfaces that are (intrinsically) isometric to it; this family is called the associate family. Conversely, two isometric minimal surfaces are associate. We will study a generalisation of this result when the ambient manifold is a Riemannian product $latex S^2\times\mathbf{R}$ or $latex H^2\times\mathbf{R}$ (where $latex S^2$ and $latex H^2$ respectively denote the constant curvature sphere and the hyperbolic plane). For this purpose we will make a connection between this problem and the study of a system of two partial differential equations.