Geodesic
Bianchi congruences of two-dimensional surfaces in~$E^4$
Sbornik. Mathematics, Tome 196 (2005) no. 10, pp. 1473-1493

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Pseudospherical Bianchi congruences in Euclidean 4-space $E^4$ are considered. The focal surfaces of such congruences are shown to have a constant negative Gaussian curvature. A geometric and an analytic description of special pseudo-spherical surfaces in $E^4$ admitting a Bianchi congruence are obtained. 
@article{SM_2005_196_10_a2,
     author = {V. A. Gorkavyy},
     title = {Bianchi congruences of two-dimensional surfaces in~$E^4$},
     journal = {Sbornik. Mathematics},
     pages = {1473--1493},
     publisher = {mathdoc},
     volume = {196},
     number = {10},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2005_196_10_a2/}
}
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V. A. Gorkavyy. Bianchi congruences of two-dimensional surfaces in~$E^4$. Sbornik. Mathematics, Tome 196 (2005) no. 10, pp. 1473-1493. http://geodesic.mathdoc.fr/item/SM_2005_196_10_a2/