Quaternionic approach on constant angle surfaces in S2 × R

Abstract

A helix surface or constant angle surface is a surface whose unit normal vector field forms a constant angle with a fixed field of directions of the ambient space. In this paper we study surfaces in S2 × R for which the unit normal makes a constant angle with the R-direction. The main idea is to show that a constant angle surface in S2 × R can be obtained by a quaternion product and a matrix representation. Also we give some related examples with figures of projections of obtained surfaces. © 2019, Tsing Hua University. All rights reserved.