On the Bour’s Theorem with Respect to Conformal Map in Minkowski Space

Abstract

A generalized helicoid and a rotational surface have a isometric relation by Bour’s theorem. It is that ”A generalized helicoid is isometric to a rotational surface. Hence, helices on the helicoid correspond to parallel circles on the rotational surface under the isometric transformation. In this study, we give a conformal relation between a generalized helicoid and a spiral surface in 3 dimensional Minkowski space . In this sitiutation, we can say that helices on the helicoid correspond to spirals on the spiral surface under the conformal transformation. Also, some related figures are given.