Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 49, No. 1, pp. 107123 (2008) 

On the twistor bundle of De Sitter space $\DS$Eduardo HulettFacultad de Matemática, Astronomía y Física, FaMAFCIEM, Ciudad Universitaria, 5000 Córdoba, Argentina, email:hulett@famaf.unc.edu.arAbstract: We study the twistor bundle $\cal{Z}$ over De Sitter space $\DS$. Viewing $\cal{Z}$ as an $SO(1,1)$principal bundle over the Grassmannian $G_2(\bb{L}^4)$ of oriented spacelike planes in LorentzMinkowski $4$space, the orthogonal complement of the fibers of $\pi':\cal{Z}\to G_2(\bb{L}^4)$ defines a 4dimensional horizontal neutral (of signature $(++)$) distribution $\cal{H} \subset T\cal{Z}$. Two $SO(3,1)$invariant almost CauchyRiemann structures $ \cal{J}^I$ and $ \cal{J}^{II}$ on $\cal{H}$ are introduced. According to which structure is considered two classes of horizontal holomorphic maps arise. These maps are projected to $\DS$ onto spacelike surfaces with different properties. We characterize both classes of horizontal maps in terms of the geometry of their projections to $\DS$. Keywords: De Sitter spacetime, twistor bundle, harmonic maps, holomorphic structures Classification (MSC2000): 53C43, 53C42, 53C28 Full text of the article:
Electronic version published on: 26 Feb 2008. This page was last modified: 28 Jan 2013.
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