Non-degenerate Bertrand Curves In Anti De Sitter 3-Space

Anti de Sitter space is a Lorentzian spatial model with negative constant sectional curvature. In relativity theory, Anti de Sitter space, which is one of the vacuum solutions in Einstein equations and has positive energy representative, is an important research object in theoretical physics. The study of curves in Anti de Sitter space not only has specific physical background, but has significant theoretical meanings in mathematics. This paper will investigate basic properties of non-degenerate Bertrand curve in three dimensional Anti de Sitter space. We also consider the relationships between non-degenerate Bertrand curves in Anti de Sitter space and R⁴₂.In the first chapter, the basic definitions and fundamental theorems of non-degenerate curves in three dimensional Anti de Sitter space will be introduced.Chapter two consists of three sections. In the first section we give definitions of timelike Bertrand curves in Anti de Sitter 3-space and study their properties. Moreover, the main results will be provided in the second section.Finally, in the third section, the definitions of spacelike Bertrand curves in R42will be introduced and the relationship between the timelike Bertrand curve in Anti de Sitter 3-space and the spacelike Bertrand curve in R42will be studied.There are three sections in the third chapter. Firstly, In section one, definitions of fist kind spacelike Bertrand curves in Anti de Sitter 3-space and their properties will be given. Moreover, we show the result in section two. Finally, we give the definitions of timelike Bertrand curves in R42and consider the relationship between the first kind spacelike Bertrand curve in Anti de Sitter 3-space and the timelike Bertrand curve in R42in the last section.In the last chapter, there are two sections. The first section will give definitions of second kind Bertrand curves in Anti de Sitter 3- space and show their properties. The main results will be given in the last section.