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Geometriae Dedicata

, Volume 154, Issue 1, pp 133–160 | Cite as

Einstein homogeneous bisymmetric fibrations

  • Fátima Araújo
Original Paper

Abstract

We consider a homogeneous fibration G/LG/K, with symmetric fiber and base, where G is a compact connected semisimple Lie group and L has maximal rank in G. We suppose the base space G/K is isotropy irreducible and the fiber K/L is simply connected. We investigate the existence of G-invariant Einstein metrics on G/L such that the natural projection onto G/K is a Riemannian submersion with totally geodesic fibers. These spaces are divided in two types: the fiber K/L is isotropy irreducible or is the product of two irreducible symmetric spaces. We classify all the G-invariant Einstein metrics with totally geodesic fibers for the first type. For the second type, we classify all these metrics when G is an exceptional Lie group. If G is a classical Lie group we classify all such metrics which are the orthogonal sum of the normal metrics on the fiber and on the base or such that the restriction to the fiber is also Einstein.

Keywords

Einstein metric Bisymmetric fibration Totally geodesic fiber Generalized symmetric space Casimir operator 

Mathematics Subject Classification (2010)

53C25 53C30 53C20 53C35 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.School of MathematicsThe University of EdinburghEdinburghUK

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