Geodesic
An Example of Bianchi Transformation in $E^4$
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2012) no. 3, pp. 240-247 
V. A. Gorkavyy. An Example of Bianchi Transformation in $E^4$. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 8 (2012) no. 3, pp. 240-247. http://geodesic.mathdoc.fr/item/JMAG_2012_8_3_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We describe a particular class of pseudo-spherical surfaces in $E^4$ which admit Bianchi transformations.

[1] Yu.A. Aminov, Geometry of Submanifolds, Gordon Breach Science Publ., Amsterdam, 2001 | MR | Zbl

[2] K. Tenenblat, Transformations of Manifolds and Applications to Differential Equations, Wiley, New York, 1998 | MR

[3] Nonlinearity Geometry. Luigi Bianchi Days, eds. D. Wojcik and J. Cieslinski, Polish Scientific Publishers PWN, Warsawa, 1998 | MR

[4] Yu. Aminov, “A Bianchi Transformation for a Domain of the Many-Dimensional Lobachevski Space”, Ukr. Geom. Sb., 21 (1978), 3–5 (Russian) | MR | Zbl

[5] L.A. Masaltsev, “Pseudo-Spherical Congruence in $E^{2n-1}$”, Mat. fiz., analiz, geom., 1:3/4 (1994), 505–512 (Russian) | MR | Zbl

[6] Yu. Aminov and A. Sym, “On Bianchi and Backlund Transformations of Two-Dimensional Surfaces in $E^4$”, Math. Phys., Anal. Geom., 3:1 (2000), 75–89 | DOI | MR | Zbl

[7] V.A. Gorkavyy, “Bianchi Congruences for Surfaces in $E^4$”, Mat. Sb., 196:10 (2005), 79–102 (Russian) | DOI | MR

[8] V.A. Gorkavyy and O.M. Nevmerzhitska, “An Analogue of the Bianchi Transformation for Two-Dimensional Surfaces in $S^3\times R^1$ and $H^3\times R^1$”, Proceedings of the International conference “Geometry in ‘`large”, topology and applications’', dedicated to A.V. Pogorelov, “Acta”, Kharkiv, 2010, 186–195