On Pseudospherical Surfaces in E⁴ with Grassmann Image of Prescribed Type - Gorkavyy, V. (Журнал математической физики, анализа, геометрии, 2006)
It is demonstrated that there exist surfaces of constant negative Gauss curvature in E⁴ whose Grassmann image consists of either hyperbolic or parabolic or elliptic points. As a consequence, there exist surfaces of constant negative Gauss curvature in E⁴ which do not admit Backlund transformations with help of pseudospherical congruencies. A geometric representation for pseudospherical surfaces in E⁴ with parabolic Grassmann image is proposed.