caa a22 4500 445884002 CHVBK 20180317145553.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s10711-010-9572-x doi (NATIONALLICENCE)springer-10.1007/s10711-010-9572-x Araújo Fátima School of Mathematics, The University of Edinburgh, JCMB, The Kings Buildings, EH9 3JZ, Edinburgh, UK aut Einstein homogeneous bisymmetric fibrations [Elektronische Daten] [Fátima Araújo] We consider a homogeneous fibration G/L → G/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. Springer Science+Business Media B.V., 2011 Einstein metric nationallicence Bisymmetric fibration nationallicence Totally geodesic fiber nationallicence Generalized symmetric space nationallicence Casimir operator nationallicence Geometriae Dedicata Springer Netherlands 154/1(2011-10-01), 133-160 0046-5755 154:1<133 2011 154 10711 https://doi.org/10.1007/s10711-010-9572-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10711-010-9572-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Araújo Fátima School of Mathematics, The University of Edinburgh, JCMB, The Kings Buildings, EH9 3JZ, Edinburgh, UK aut NATIONALLICENCE 773 0- Geometriae Dedicata Springer Netherlands 154/1(2011-10-01), 133-160 0046-5755 154:1<133 2011 154 10711 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer