Spacelike surfaces in De Sitter space S^3_1 via twistor lifts

EDUARDO HULETT

Novi Sad, Serbia.

Congreso; 12th Serbian Congress of Mathematics, Novi Sad, Serbia; 2008

University of Novi Sad, University of Beograd

We describe some relevant aspects of the geometry of the twistor bundle Z over De Sitter 3-space S^3_1. As a homogeneous bundle Zt is equipped with a non-integrable invariant 4-dim distribution H of contact type. H happens to support two invariant almost invariant complex structures which in turn give rise to corresponding almost CR structures on Z. The behaviour of twistor lifts of space like surfaces in S^3_1 is considered in relation to these structures. Some interesting classes of surfaces arise from this geometric structure. Examples are discussed.