Standard homogeneous Einstein manifolds and Diophantine equations
by
E.D. Rodionov
Barnaul State Pedagogical University

A classification of the simply connected compact standard homogeneous Einstein manifolds either with a simple transitive group of motions or with a simple isotropy subgroup was given by W.Ziller-W.McKenzie and E.D.Rodionov . In this paper some new examples of standard homogeneous Einstein manifolds with semisimple transitive groups of motions and semisimple isotropy subgroups are constructed. For the construction of these examples the solutions of some systems of Diophantine equations are used. These investigations are supported by a grant from the Russian Fund of Fundamental Investigations (grant 99-01-00543) and a grant from the S.-Petersburg University (grant 97-0-1.3-63).

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McKenzie, Y.W., Ziller, W., On normal homogeneous Einstein manifolds, Ann. Sci. Ecole Norm. Sup. (4) 18 (1985), 563-633.

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Rodionov, E.D., Standard homogeneous Einstein manifolds, Russian Acad. Sci. Dokl. Math. 47 (1993), no.1, 37-40.

Date received: February 26, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadw-44.