Degenerate Bianchi transformations for three-dimensional pseudo-spherical submanifolds in ${\mathbb{R}}^5$

Abstract

Three-dimensional pseudo-spherical submanifolds in ${\mathbb{R}}^5$, whose Bianchi transformations are degenerate of rank 2, are studied. A complete description of such submanifolds is obtained in the case where the Bianchi transformations are holonomically degenerate.