2018
Том 70
№ 7

All Issues

Gor'kavyi V. A.

Articles: 4
Article (Russian)

Birosettes are model flexors

Gor'kavyi V. A., Milka A. D.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 7. - pp. 885-904

A new family of polyhedra called birosettes is presented. The geometric features of birosettes are analyzed. The model flexibility of birosettes is explained.

Article (Russian)

Degenerate Backlund transformation

Gor'kavyi V. A., Nevmerzhitskaya E. N.

↓ Abstract

Ukr. Mat. Zh. - 2016. - 68, № 1. - pp. 38-51

A concept of degenerate B¨acklund transformation is introduced for two-dimensional surfaces in many-dimensional Euclidean spaces. It is shown that if a surface in $R^n, n \geq 4$, admits a degenerate B¨acklund transformation, then this surface is pseudospherical, i.e., its Gauss curvature is constant and negative. The complete classification of pseudospherical surfaces in $R^n, n \geq 4$ that admit degenerate Bianchi transformations is obtained. Moreover, we also obtain a complete classification of pseudospherical surfaces in $R^n, n \geq 4$, admitting degenerate Backlund transformations into straight lines.

Article (Russian)

Two-dimensional pseudospherical surfaces with degenerate Bianchi transformation

Gor'kavyi V. A., Nevmerzhitskaya E. N.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2011. - 63, № 11. - pp. 1460-1468

We classify two-dimensional pseudospherical surfaces with degenerate Bianchi transformation in a multidimensional Euclidean space.

Chronicles (Ukrainian)

International Conference on Geometry "in the Large"

Diskant V. I., Gor'kavyi V. A., Milka A. D.

Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 7. - pp. 1007-1008