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Homogeneous Kähler and Sasakian structures related to complex hyperbolic spaces

Part of: Global differential geometry

Published online by Cambridge University Press:  30 April 2010

P. M. Gadea  and
J. A. Oubiña
P. M. Gadea
Affiliation:
Instituto de Física Fundamental, CSIC, Serrano 113-bis, 28006 Madrid, Spain (pmgadea@iec.csic.es)
J. A. Oubiña
Affiliation:
Departamento de Xeometría e Topoloxía, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain (ja.oubina@usc.es)
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Abstract

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We study homogeneous Kähler structures on a non-compact Hermitian symmetric space and their lifts to homogeneous Sasakian structures on the total space of a principal line bundle over it, and we analyse the case of the complex hyperbolic space.

Keywords

homogeneous Riemannian structureshomogeneous Kähler structureshomogeneous almost-contact Riemannian manifoldsnon-compact Hermitian symmetric spacesSasakian spaces

MSC classification

Secondary: 53C30: Homogeneous manifolds 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.) 53C35: Symmetric spaces 53C55: Hermitian and Kählerian manifolds
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 53 , Issue 2 , June 2010 , pp. 393 - 413
Copyright
Copyright © Edinburgh Mathematical Society 2010