Conformal homogeneous spacelike surfaces in 3-dimensional Lorentz space forms

Abstract

Let M13(c) be an 3-dimensional Lorentz space form and C(M13(c)) denote the conformal transformation group of M13(c). A spacelike surface x:M2→M13(c) is called a conformal homogeneous spacelike surface. If there exists a subgroup G⊂C(M13(c)) such that the orbit G(p)=x(M2),p∈x(M2). In this paper, we classify completely conformal homogeneous spacelike surfaces up to a conformal transformation of M13(c).