Bour’s Theorem of Spacelike Surfaces in Minkowski 4-Space

Abstract

In this paper, we study on three kinds of spacelike helicoidal surfaces in Minkowski 4-space. First, we give an isometry between such helicoidal surfaces and rotational surfaces which is a kind of generalization of Bour’s theorem in Minkowski 3-space to Minkowski 4-space. Then, we show that if the isometric pair of surfaces have same Gauss map, then they are hyperplanar and minimal. Also, we give the parametrizations of isometric pair of surfaces having same Gauss map. Finally, we present some examples via Wolfram Mathematica 10.4.