Rotation Surfaces In 3-Dimensional Anti-de Sitter Space

In this paper, we discuss the existence problem of rotation surfaces of given Gauss curvature function in H₁³(-1) and give the position vector field of the surfaces. Simultaneously, we study the existence problem of a special Weingarten rotation surfaces in H₁³( -1) and give all spacelike and timelike Weingarten rotation surfacesin H₁³(-1) using the parametric representation of rotation surfaces.This paper is divided into four sections. In section one, the historical background of the relevant problems is presented and the mainly results are introduced. Section two is preliminaries, some basic definitions and properties related to these results are introduced in this section. In section three, we mainly discuss the existence problemof rotation surfaces of given Gauss curvature function in H₁³(-1) and give theposition vector field of the surfaces and obtain theorem one and theorem two. In the fourth section, we stress on the study of the existence problem of a special Weingartenrotation surfaces in H₁³( -1) and give all spacelike and timelike Weingarten rotation surfaces in H₁³( -1) ,and obtain three theorem.