Split Quaternions and Spacelike Constant Slope Surfaces in Minkowski 3-Space

Details Split Quaternions and Spacelike Constant Slope Surfaces in Minkowski 3-Space Split Quaternions and Spacelike Constant Slope Surfaces in Minkowski 3-Space

2012-03-03

arxiv.org/abs/1203.0688v1

Physics

Mathematical Physics

13 pages, 2 figures

Scientific paper

A spacelike surface in the Minkowski 3-space is called a constant slope surface if its position vector makes a constant angle with the normal at each point on the surface. These surfaces completely classified in [J. Math. Anal. Appl. 385 (1) (2012) 208-220]. In this study, we give some relations between split quaternions and spacelike constant slope surfaces in Minkowski 3-space. We show that spacelike constant slope surfaces can be reparametrized by using rotation matrices corresponding to unit timelike quaternions with the spacelike vector parts and homothetic motions. Subsequently we give some examples to illustrate our main results.

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