Orthogonal Nets and Cliiord Algebras
نویسنده
چکیده
A Cliiord algebra model for MM 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.
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