The exact concepts of the dividing surface related to the metrics of an arbitrarily curved surface layer and the transverse surface tension as the excess surface value with respect to the normal component of stress tensor were introduced. It was shown that, in the absence of external fields, there will be a dividing surface in a slightly curved surface layer. This dividing surface satisfies the zero value of transverse surface tension and coincides with the tension surface. When external fields are present, the tensors of excess surface and linear stresses are three-dimensional parameters, whose dimensions generally cannot be diminished by the selection of the positions of dividing surfaces and lines. At the same time, the conditions of mechanical equilibrium for curved surfaces can be formulated without using the transverse surface tension. The conditions of mechanical equilibrium at the contact line include the transverse tension of a line and the normal components of linear tension.