Abstract

We consider smooth Riemannian surfaces whose curvature K satisfies the eguationAlogK-c=aK+b away from points where K=c for some (a,b, c) eIR3, which we callgeneralized Ricci surfaces. This equation generalize a result of Ricci, which provides a necessaryand sufficient condition for the surface to be (locally) minimally and isometrically immersed inEuclidean 3-space. in the first part of this talk, we prove some basic properties of generalized Riccisurfaces, in order to show that these surfaces are related to many geometric objects. in the secondpart, we mainly focus on compact generalized Ricci surfaces: we obtain topological obstructionsand construct examples. This is a joint work with Benoit Daniel..