An algebraic representation of the affine Bäcklund transformation (Q1205424)

Concerning the affine Bäcklund transformation, which is defined for affine minimal (maximal) surfaces, the author shows that it has an especially simple characterization in terms of the integral representations developed previously by \textit{W. Blaschke}, in ``Vorlesungen über Differentialgeometrie'', Vol. II, Springer (Berlin, 1923), for the hyperbolic case, and \textit{E. Calabi}, in Result. Math. 13, No. 3/4, 199-223 (1988; Zbl 0653.53006)] for the elliptic case. In either instance, it consists of an involution and translation in the appropriate parameter space. Moreover, he further shows that the range of affine Bäcklund transformations of an affine minimal (maximal) surface, hyperbolic or elliptic, does not change after two compositions of affine Bäcklund transformations.