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

作者：Hulett Eduardo^*

来源：Differential Geometry and its Applications, 2010, 28(6): 656-671.

DOI：10.1016/j.difgeo.2010.08.001

• De Sitter 3-space
• Twistor bundle
• Harmonic maps
• Twistor lift
• Holomorphic map
• Constant mean curvature

We deal here with the geometry of the so-called twistor fibration Z -> S(1)(3) over the De Sitter 3-space, where the total space Z is a five-dimensional reductive homogeneous space with two canonical invariant almost CR structures. Fixed the normal metric on Z we study the harmonic map equation for smooth maps of Riemann surfaces into Z. A characterization of spacelike surfaces with harmonic twistor lifts to Z is obtained. Also it is shown that the harmonic map equation for twistor lifts can be formulated as the curvature vanishing of an S(1)-loop of connections i.e. harmonic twistor lifts exist within S(1)-families. Special harmonic maps such as holomorphic twistor lifts are also considered and some remarks concerning (compact) vacua of the twistor energy are given.

• 出版日期2010-12