On Guichards nets and Cyclic systems

Summary In the rst part we give a self contained introduction to the theory of cyclic systems in ndimensional space which can be considered as immersions into certain Grassmannians We show how the metric geometries on spaces of constant curvature arise as subgeometries of Mobius geometry which provides a slightly new viewpoint In the second part we characterize Guichard nets which are given by cyclic systems as being Mobius equivalent to parameter families of linear Weingarten surfaces This provides a new method to study families of parallel Weingarten surfaces in space forms In particular analogs of Bonnet s theorem on parallel constant mean curvature surfaces can be easily obtained in this settin