Isometries between minimal helicoidal surfaces and rotation surfaces in minkowski space

Abstract

In Minkowski 3-space, a helicoidal surface is a generalization of rotation surface, which is somewhat similar except the translation part. Therefore, a natural question arises whether an isometry between these surfaces exists. It is proved that, in Minkowski 3-space, a minimal helicoidal surface with Gauss curvature K has an isometric minimal rotation surface if and only if K⩽0. Especially, we show that a timelike right helicoid does not have an isometric minimal rotation surface.