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On Compact 7-dimensional Einstein Homogeneous Manifolds
by
Yu.G. Nikonorov
Altai State University, Rubtsovsk Industrial Institute
It is well known, that any homogeneous Einstein manifold Mn of dimension 2 or 3 is isometric to the space of constant sectional curvature. As was shown by G.Jensen, any M4 is symmetric space [1]. The complete classification of 5-dimensional compact homogeneous spaces with invariant Einstein metric was obtained by D.Alekseevsky, Isabel Dotti and C. Ferraris [2]. The classification of compact homogeneous Einstein manifold of dimension 6 was found by Eu.Rodionov and Yu.Nikonorov [3].
In this paper we present the classification of compact 7-dimensional homogeneous spaces with invariant Einstein metric.
The work was supported by RFBR (grants N 99-01-00543, 96-15-96291) and by the grant N 97-0-1.3-63 of St.-Peterburg State university.
References
[1] G.R.Jensen. Homogeneous Einstein spaces of dimension 4. J. Differential Geom. 3(1969), 309-349.
[2] D.Alekseevsky, Isabel Dotti and C.Ferraris. Homogeneous Ricci positive 5-manifolds. Pacific Journal of Mathematics 175(1996), 1-12.
[3] Yu.G.Nikonorov, Eu.D.Rodionov. Compact 6-dimensional homogeneous Einstein manifolds. Doklady RAN, 365(1999), 599-601.
Date received: January 25, 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-07.