Геометрические исследования поверхностей зонтичного типа

Geometrical Investigations of Umbrella Surfaces

Umbrella shells are used as coverings of civil and industrial buildings. Umbrella surfaces are formed on surfaces of revolution. Several new types of umbrella surfaces are presented in the article. Base surfaces of revolution were chosen in the form of spheres and paraboloids of revolution. The coefficients of the first and second fundamental forms of surface are derived for presented surfaces. All of the surfaces contain the areas both of negative and positive total curvature.