Resumen de On the geometry of the Painlevé V equation and a Bäcklund transformation

W.K. Schief

• It is shown that an integrable class of helicoidal surfaces in Euclidean space E3 is governed by the Painlevé V equation with four arbitrary parameters. A connection with sphere congruences is exploited to construct in a purely geometric manner an associated Bäcklund transformation.