Potapenko I. V.
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 $E_3$.
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.
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 $E_3$.
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.