# Spacelike surfaces in De Ditter 3-space and their twistor lifts - Mathematics > Differential Geometry

Spacelike surfaces in De Ditter 3-space and their twistor lifts - Mathematics > Differential Geometry - Download this document for free, or read online. Document in PDF available to download.

Abstract: We deal here with the geometry of the twistor fibration $\mathcal{Z} \to\bb{S}^3 1$ over the De Sitter 3-space. The total space $\mathcal{Z}$ is a fivedimensional reductive homogeneous space with two canonical invariant almost CRstructures. Fixed the normal metric on $\mathcal{Z}$ we study the harmonic mapequation for smooth maps of Riemann surfaces into $\mathcal{Z}$. Acharacterization of spacelike surfaces with harmonic twistor lifts to$\mathcal{Z}$ is obtained. It is also shown that the harmonic map equation fortwistor lifts can be formulated as the curvature vanishing of an$\bb{S}^1$-loop of connections i.e. harmonic twistor lifts exist within$\bb{S}^1$-families. Special harmonic maps such as holomorphic twistor liftsare also considered and some remarks concerning compact vacua of the twistorenergy are given.

Author: ** Eduardo Hulett**

Source: https://arxiv.org/