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

2009/10/29 by Hulett, Eduardo
#53C42 #53C43 (Primary) #53C50 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0910.5626

Abstract

We deal here with the geometry of the twistor fibration Z → \bbS³₁ over the De Sitter 3-space. 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. It is also shown that the harmonic map equation for twistor lifts can be formulated as the curvature vanishing of an \bbS¹-loop of connections i.e. harmonic twistor lifts exist within \bbS¹-families. Special harmonic maps such as holomorphic twistor lifts are also considered and some remarks concerning (compact) vacua of the twistor energy are given.

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• Harmonic maps and twistorial structures
• The twistor lifts of surfaces in 4-spaces
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• Harmonic morphisms between Weyl spaces and twistorial maps II