This article is cited in 10 papers

Bianchi congruences of two-dimensional surfaces in $E^4$

V. A. Gorkavyy

B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine

Abstract: 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.

UDC: 514

MSC: Primary 53A07, 53A25; Secondary 37K35

Received: 17.05.2004 and 15.04.2005

DOI: 10.4213/sm1426

 English version: Sbornik: Mathematics, 2005, 196:10, 1473–1493

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