2019
Том 71
№ 6

# Potapenko I. V.

Articles: 4
Article (Ukrainian)

### Relationship between normalized tensors of two regular networks on the surfaces in the Euclidean space $E_3$

Ukr. Mat. Zh. - 2016. - 68, № 2. - pp. 271-277

We establish the relationship between the normalized tensors of two regular networks on the surfaces in the Euclidean space $E_3$.

Article (Ukrainian)

### Leiko Network on the Surfaces in the Euclidean Space $E_3$

Ukr. Mat. Zh. - 2015. - 67, № 6. - pp. 820–828

We introduce the notion of Leiko network as a generalization of the geodetic network on the surfaces of nonzero Gaussian curvature in the Euclidian space $E_3$ and study its characteristics. The conditions of preservation of the Leiko network under infinitesimal deformations of the surfaces are also obtained.

Article (Ukrainian)

### On the reconstruction of the variation of the metric tensor of a surface on the basis of a given variation of christoffel symbols of the second kind under infinitesimal deformations of surfaces in the euclidean space $E_3$

Ukr. Mat. Zh. - 2011. - 63, № 4. - pp. 523-530

We investigate the problem of reconstruction of variation of a metric tensor of a surface on the basis of given variation of the sekond-kind Christoffel symbols for infinitesimal deformations of surfaces in the Euclidean space $E_3$.

Article (Ukrainian)

### New equations of infinitesimal deformations of surfaces in $E_3$

Ukr. Mat. Zh. - 2010. - 62, № 2. - pp. 199–202

We establish a condition for two symmetric tensor fields that is necessary and sufficient for the existence of a displacement vector in the case of infinitesimal deformation of a surface in the Euclidean space E 3.