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

Authors

Sungwook Lee, University of Connecticut

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 S³1 is obtained. The formula is used to investigate a correspondence between CMC 1 space-like surfaces in S³1 and maximal space-like surfaces in the Minkowski 3-space L³ . Three types of Gauss maps are discussed, and their relationships to each other are investigated. The Weierstrass type representation formula f0=ℜez0

z

1 2h1+g² ,i 2h1-g² ,-hg dz for the maximal space-like immersion f ₀ in the Minkowski 3-space L³ can be obtained as the limit surface of CMC c ( c > 0) space-like surfaces in de Sitter 3-space S³1 (c²) of constant positive sectional curvature c², as the complex Lie group SL(2, C ) collapses into the abelian group C³ . A duality property of CMC 1 space-like surfaces in S³1 is also obtained and studied. Some examples of CMC 1 space-like surfaces in S³1 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://digitalcommons.lib.uconn.edu/dissertations/AAI3071211