Resumen de On Closed Weingarten Surfaces

Wolfgang Kühnel, Michael Steller

• We investigate closed surfaces in Euclidean 3-space satisfying certain functional relations ? = F(?) between the principal curvatures ?, ?. In particular we find analytic closed surfaces of genus zero where F is a quadratic polynomial or F(?) = c?2n+1. This generalizes results by H. Hopf on the case where F is linear and the case of ellipsoids of revolution where F(?) = c?3.