On closed weingarten surfaces

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