The Contact Angle Of Immersed Surfaces In The Anti-de Sitter Space H₁²ⁿ⁺¹

In this paper we mainly discuss some properties about the contact angle and the holomorphic angle of immersed surfaces in the anti-de Sitter space H2n+11. This paper has been divided into two chapters.In chapter one, we sum up the former scholar'study works in the contact angle, give a brief of the results in this paper and some prior knowledge.The second chapter has been divided into four sections. In section one, by em-ploying the moving frames, we get the formulas of the Gauss curvature K and Laplace operator△of the great spacelike immersed surfaces on the contact angle β and the holomorphic angle a in the anti-de Sitter space H2n+11. In section two, we argue some properties of compact connected great spacelike surfaces in H51, when the holomor-phic angle α=0. In section three, we get the general expression about the Gauss curvature of the great spacelike immersed surfaces when the contact angle β=0. In section four,we argue the case of the immersed surfaces when the contact angle β and holomorphic angle a are constant.