On Pseudospherical Surfaces in E4 with Grassmann Image of Prescribed Type

Анотація

It is demonstrated that there exist surfaces of constant negative Gauss curvature in $E^4$ whose Grassmann image consists of either hyperbolic or parabolic or elliptic points. As a consequence, there exist surfaces of constant negative Gauss curvature in $E^4$ which do not admit Backlund transformations with help of pseudospherical congruencies. A geometric representation for pseudospherical surfaces in $E^4$ with parabolic Grassmann image is proposed.

Mathematics Subject Classification: 53A07, 53A25, 53B25.