BOUR'S THEOREM UNDER THE CONFORMAL MAP WITH LIGHT LIKE PROFILE CURVE

A generalized helicoid and a rotational surface have an isometric relation by Bour's theorem. It is that "A generalized helicoid is isometric to a rotational surface. Hence, helices on the helicoid can be transformed to parallel circles on the rotational surface under the isometric transformation". In this study, we give a conformal relation between a generalized helicoid (with lightlike profile curve) and a spiral surface (with lightlike profile curve). In this sitiutation, we can say that helices on the helicoid can be transformed to spirals on the spiral surface under the conformal transformation. Also, some related examples and their figures are given. 2000 Mathematics Subject Classification. 53A05, 53C10S