On Some Properties of k-surface without Torsion in (n+k)-dimensional Euclidean Space

In multidimensional Euclidean spaces, normal torsion coefficients for k-surfaces are considered, which are determined through the normal bundles of these surfaces. The main goal of this article is to study the properties of k-surfaces in the space E^(n+k), which have a codimension greater than 1, and whose torsion coefficients in the canonical basis of normal space are equal to zero. The article uses methods of differential and Riemannian geometry, as well as tensor analysis tools to study n-surfaces with codimension different from unity. Explores the relationship between the properties of n-surfaces and the corresponding two-dimensional surfaces that belong to (n+2)-dimensional Euclidean space. We also consider n-surfaces that do not have torsion in (n+k)-dimensional Euclidean space, for which it is proven that in the neighborhood of any axial point M one can find a region where the only axial point is precisely this point M.