Geometry Research Group

V.N. Karazin Kharkiv
National University

Склад секції

Alexander L. Yampolsky Docent (associate professor) of department of fundamental mathematics, z, doctor of sciences in physics and mathematics, docent (associate professor)

Kostiantyn D. Drach Phd in mathematics

Olga V. Lykova Phd in mathematics, senior lecturer

Olena M. Nevmerzhitska Phd in mathematics, senior lecturer

Eugene V. Petrov Phd in mathematics, senior lecturer

Olena O. Shugailo Phd in mathematics, senior lecturer

Dmytro V. Bolotov Doctor of sciences in physics and mathematics, senior researcher of iltpe

Vasyl O. Gorkavyy Doctor of sciences in physics and mathematics, docent (associate professor)

. Docent (associate professor) of department of theoretical and applied computer science , phd in mathematics, docent (associate professor)

P. G. Dolya Docent (associate professor) of department of theoretical and applied computer science , phd for industries

Iryna V. Kats Lead engineer

Dm. I. Vlasenko Phd in mathematics, senior lecturer

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A.L. Yampolsky

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Olena M. Nevmerzhitska

Phd in mathematics, senior lecturer

List of selected publications

V.O. Gorkavyy and O.M. Nevmerzhitska Ruled surfaces as pseudo-spherical congruences (russian) // Proc. Intern. Geom. Center 2009 2(2) 21–37, 2009 2(2) 21–37, 2009

Given a two-dimensional ruled surfaces in one of spaces E^n, S^n, H^n, S^n×R^1, H^n×R^1, shift mappings at constant distance along rulings are considered. It is shown, that no ruled surface in E^n, H^n, H^n×R^1 generates pseudo-spherical congruencies (Bianchi-Backlund transformations) with the help of the shift mappings. On the other hand, it is proved that a shift mapping of a ruled surface in either S^n or S^n×R^1 represents a pseudo-spherical congruence if and only if the surface in question is intrinsically flat and has a constant negative extrinsic curvature. Moreover, an analytical description of the ruled surfaces with vanishing intrinsic curvature and with constant negative extrinsic curvature is discussed.

Keywords: Pseudospherical Congruences

V.O. Gorkavyy and O.M. Nevmerzhitska Ruled Surfaces as Pseudospherical Congruences // Journal of Mathematical Physics, Analysis, Geometry, 2009, Vol. 5, №.4, p. 359 – 374.,

Two-dimensional ruled surfaces in the spaces of constant curvature R^n, S^n, H^n and in the Riemannian products S^n x R^1, H^n x R^1 are considered. A ruled surface is proved to represent a pseudospherical congruence if and only if it is either an intrinsically flat surface in S^n, or an intrinsically flat surface with constant extrinsic curvature in S^n X R^1.

Keywords: pseudo-spherical congruence, ruled surface

V.O. Gorkavyy and O.M. Nevmerzhitska En analogue of the Bianchi transformation for two-dimencional surfaces in S^3 x R^1 (russ.) // Mathematical notes (russ.), 2011, Том 89, №.6, С. 833 – 845.,

In this paper, we build Bianchi type transformation for two-dimensional surfaces of constant negative inner curvature of space S^3 x R^1

Keywords: Bianchi type transformation

V.O. Gorkavyy and O.M. Nevmerzhitska Pseudo-spherical submanifolds in Euclidean space with degenerated Bianchi transformation. // Reports of the National Academy of Sciences of Ukraine, 2010, 2010, №.6,

Keywords: Pseudo-spherical submanifold, pseudo-spherical congruence, Bianchi transformation

V.O. Gorkavyy and O.M. Nevmerzhitska En analogue of the Bianchi transformation for two-dimencional surfaces in S^3 x R^1 (russ.) // Proceedings of the International Conference "Geometry" in general ", Topology and its applications", 2010, C.186 – 195,

Keywords: Bianchi type transformation

V. Gorkavyy, O. Nevmerzhitska Pseudo-spherical submanifolds with degenerate Bianchi transformation // Results in Mathematics, 2011, V.60, №.1, P.103 – 116,

Gorkavyy V. Pseudo-spherical submanifolds with degenerate Bianchi transformfation

Keywords: Pseudo-spherical submanifolds, Bianchi transformation

V.O. Gorkavyy and O.M. Nevmerzhitska Pseudo-spherical submanifolds in Euclidean space with degenerated Bianchi transformation (russ.). // Ukrainian Mathematical Journal, Том 63, 2011, с.1461-1468.,

A complete descriptions of pseudo-spherical submanifolds in Euclidean space with Bianchi transformation degenerated into curve is obtained.