Spacelike surfaces in De Sitter $3$-space and their twistor lifts

EDUARDO HULETT

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2010 vol. 28 p. 656 - 671

0926-2245

We deal here with the geometry of the so-called twistor fibration over the De Sitter 3-space, where the total space is a five-dimensional reductive homogeneous space with two canonical invariant almost CR structures. Fixed the normal metric on we study the harmonic map equation for smooth maps of Riemann surfaces into . A characterization of spacelike surfaces with harmonic twistor lifts to is obtained. Also it is shown that the harmonic map equation for twistor lifts can be formulated as the curvature vanishing of an -loop of connections i.e. harmonic twistor lifts exist within -families. Special harmonic maps such as holomorphic twistor lifts are also considered and some remarks concerning (compact) vacua of the twistor energy are given.