#### Title

Space-like surfaces of constant mean curvature in de Sitter 3-space S31

#### Date of Completion

January 2002

#### Keywords

Mathematics

#### Degree

Ph.D.

#### Abstract

A Bryant type representation formula for space-like surfaces of constant mean curvature 1 (abbreviated as CMC 1) in de Sitter 3-space S^{3}1 is obtained. The formula is used to investigate a correspondence between CMC 1 space-like surfaces in S^{3}1 and maximal space-like surfaces in the Minkowski 3-space L^{3} . Three types of Gauss maps are discussed, and their relationships to each other are investigated. The Weierstrass type representation formula f0=ℜez0

- z

^{2},i 2h1-g

^{2 },-hg dz for the maximal space-like immersion

*f*

_{ 0}in the Minkowski 3-space L

^{3}can be obtained as the limit surface of CMC

*c*(

*c*> 0) space-like surfaces in de Sitter 3-space S

^{3}1 (

*c*

^{2}) of constant positive sectional curvature

*c*

^{2}, as the complex Lie group

*SL*(2, C ) collapses into the abelian group C

^{3}. A duality property of CMC 1 space-like surfaces in S

^{3}1 is also obtained and studied. Some examples of CMC 1 space-like surfaces in S

^{3}1 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. ^

#### Recommended Citation

Lee, Sungwook, "Space-like surfaces of constant mean curvature in de Sitter 3-space S31" (2002). *Doctoral Dissertations*. AAI3071211.

https://opencommons.uconn.edu/dissertations/AAI3071211