Citation/Abstract

A Bryant type representation formula for space-like surfaces of constant mean curvature 1 (abbreviated as CMC 1) in de Sitter 3-space [Special characters omitted.] is obtained. The formula is used to investigate a correspondence between CMC 1 space-like surfaces in [Special characters omitted.] and maximal space-like surfaces in the Minkowski 3-space [Special characters omitted.] . Three types of Gauss maps are discussed, and their relationships to each other are investigated. The Weierstrass type representation formula [Special characters omitted.] for the maximal space-like immersion f ₀ in the Minkowski 3-space [Special characters omitted.] can be obtained as the limit surface of CMC c ( c > 0) space-like surfaces in de Sitter 3-space [Special characters omitted.] ( c ² ) of constant positive sectional curvature c ² , as the complex Lie group SL (2, [Special characters omitted.] ) collapses into the abelian group [Special characters omitted.] . A duality property of CMC 1 space-like surfaces in [Special characters omitted.] is also obtained and studied. Some examples of CMC 1 space-like surfaces in [Special characters omitted.] are given, and are realized in the time-like open 3-ball with an indefinite metric by the standard stereographic projection. The graphs of these surfaces are generated by MATHEMATICA.