We present the classification of two-dimensional pseudospherical surfaces with degenerate Bianchi transformation in the multidimensional Euclidean space.
Similar content being viewed by others
References
Yu. A. Aminov, Geometry of Submanifolds [in Russian], Naukova Dumka, Kiev (2002).
K. Tenenblat, Transformations of Manifolds and Applications to Differential Equations, Longman, Harlow (1998).
L. A. Masal’tsev, “Pseudospherical Bianchi congruence in E 2n−1,” Mat. Fiz. Anal. Geom., 1, No. 3/4, 505–512 (1994).
Yu. Aminov and A. Sym, “On Bianchi and Bäcklund transformations of two-dimensional surfaces in E 4,” Math. Phys., Anal., Geom., 3, No. 1, 505–512 (2000).
V. A. Gor’kavyi, “Bianchi congruence of two-dimensional surfaces in E 4,” Mat. Sb., 196, No. 10, 79–102 (2005).
V. A. Gor’kavyi and E. N. Nevmerzhitskaya, “On two-dimensional pseudospherical surfaces in E 4 with degenerate Bianchi transformation,” Dopov. Nats. Akad. Nauk Ukr., No. 6, 13–18 (2010).
Author information
Authors and Affiliations
Additional information
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 11, pp. 1460–1468, November, 2011.
Rights and permissions
About this article
Cite this article
Gor’kavyi, V.A., Nevmerzhitskaya, E.N. Two-dimensional pseudospherical surfaces with degenerate Bianchi transformation. Ukr Math J 63, 1660–1669 (2012). https://doi.org/10.1007/s11253-012-0605-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-012-0605-5