1998/02/27 by Alexander I. Bobenko, Bobenko, Alexander I., Udo Hertrich-Jeromin +2
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.DG
paper · pdf · doi:10.48550/arxiv.math/9802126
Plain TeX, 16 pages, 4 pictures
arxiv created 1998/02/27 · arxiv updated 2009/11/30
A Clifford algebra model for M"obius geometry is presented. The notion of Ribaucour pairs of orthogonal systems in arbitrary dimensions is introduced, and the structure equations for adapted frames are derived. These equations are discretized and the geometry of the occuring discrete nets and sphere congruences is discussed in a conformal setting. This way, the notions of ``discrete Ribaucour congruences'' and ``discrete Ribaucour pairs of orthogonal systems'' are obtained --- the latter as a generalization of discrete orthogonal systems in Euclidean space. The relation of a Cauchy problem for discrete orthogonal nets and a permutability theorem for the Ribaucour transformation of smooth orthogonal systems is discussed.