Infinitesimally small deformation which preserves geodesic lines

This paper proves that regular right circular cylinder permits non-trivial infinitesimally small deformation, which preserves geodesic lines and any pieces of the given surface with an equal area. The above mentioned surface is uniquely defined by preliminary chosen non-zero function of a single variable and two meaningful constants. Under these conditions tensor fields are found in explicit way. Every deformation can be interpreted as momentless stressed state of cylindrical shell with a certain surface stress.