On Guichard's nets and Cyclic systems

Details On Guichard's nets and Cyclic systems On Guichard's nets and Cyclic systems

1997-04-03

arxiv.org/abs/dg-ga/9704003v1

Mathematics

Differential Geometry

25 pages, plain TeX

Scientific paper

In the first part, we give a self contained introduction to the theory of cyclic systems in n-dimensional 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 Moebius geometry which provides a slightly new viewpoint. In the second part we characterize Guichard nets which are given by cyclic systems as being Moebius equivalent to 1-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 setting.

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