Multidimensional euclidean surfaces, set by several scalar functions

Background. Nowadays, the theory of multidimensional Euclidean surfaces is actively developing. There have been investigated hypersurfaces, described by one explicit scalar function. There has been started a research of surfaces, set by several scalar functions. The aim of this work is to describe surfaces, set by several scalar functions. Materials and methods. The author considered surfaces that are an intersection of several cylindrical surfaces. Results. The author drew out tangential planes of cylindrical of surfaces and their intersections, obtained coordinates of vectors of cylindrical surface normals and their intersections and introduced expressions of coefficients of curvature forms of cylindrical surfaces through coefficients of their metric forms. For given coefficients of metric forms of surfaces, the author found cylindrical surfaces that are an intersection the set ones as the intersection of cylindrical surfaces. Conclusions. Every surface of a multidimensional Euclidean space, differring from the hypersurface and the cylindrical surface, is an intersection of cylindrical surfaces and is defined with the accuracy up to the position in space in metric forms of cylindrical surfaces.