关键词: 三维欧氏空间, 非可展直纹面, 主法线曲面, 结构函数, 腰曲线

Abstract: As special non-developable ruled surface， the normal ruled surface has good algebraic and geometric properties. Using the classical methods of differential geometry， the structure functions of the normal ruled surface in 3-D Euclidean Space are studied. According to the definition and standard equation of non-developable ruled surface in 3-D Euclidean Space， the definition and standard equation are given to the normal ruled surface. Based on the definition and standard equation of the normal ruled surface， the deep relation of the structure functions is obtained. Then some conclusions about the directrix， the striction line and the structure functions are obtained. By discussing the normal ruled surfaces of general helices and Mannheim curves in 3-D Euclidean Space， conclusions can be drawn that the normal ruled surfaces of general helices are positive spiral surfaces and the normal ruled surfaces of Mannheim curves are binormal ruled surfaces of their Mannheim partner curves.

Key words: 3-D Euclidean Space, non-developable ruled surface, normal ruled surface, structure function, striction line