2019
Том 71
№ 11

# Gor'kavyi V. A.

Articles: 4
Article (Russian)

### Birosettes are model flexors

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

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

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"

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