Dupin'sche Hyperflächen in \(E^ 4\). (Dupin hypersurfaces in \(E^ 4)\) (Q1062288)

A hypersurface in \(E^ N\) is called a Dupin hypersurface in the paper under review if along each curvature surface of M the corresponding principal curvature is constant. In \(E^ 3\) the only such surfaces are the planes, the spheres and the well-known cyclides of Dupin. In the paper under review all Dupin hypersurfaces in \(E^ 4\) are classified up to Lie transformations. For more informations on Dupin hypersurfaces see Math. Ann. 270, 427-440 (1985; Zbl 0538.53004) by the author and Bull. Lond. Math. Soc. 15, 493-498 (1983; Zbl 0529.53044) by the reviewer.