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arXiv:math.DG/0509442v223Sep2005 On the twistor space of pseudo-spheres

Summary: arXiv:math.DG/0509442v223Sep2005
On the twistor space of pseudo-spheres
R. Albuquerque1
and Isabel M.C. Salavessa2
December 21, 2005
Centro de Investiga¸c~ao em Matem´atica e Aplica¸c~oes, Universidade de ´Evora,
7000 ´EVORA, Portugal; e-mail: rpa@uevora.pt
Centro de F´isica das Interac¸c~oes Fundamentais, Instituto Superior T´ecnico, Edif´icio Ci^encia,
Piso 3, 1049-001 LISBOA, Portugal; e-mail: isabel@cartan.ist.utl.pt
Abstract: We give a new proof that the sphere S6 does not admit an integrable orthogonal
complex structure, as in [11], following the methods from twistor theory.
We present the twistor space Zp,q of a pseudo-sphere S2n
2q = SO2p+1,2q/SO2p,2q as a pseudo-
K¨ahler symmetric space. We then consider orthogonal complex structures on the pseudo-
sphere, only to prove such a structure cannot exist.
1 Introduction
This article raises some questions around the problem solved by C. Lebrun in [11] about
the non existence of orthogonal complex structures on the sphere S6


Source: Albuquerque, Rui - Departamento de Matemática, Universidade de Évora


Collections: Mathematics