Atlas: On Compact 7-dimensional Einstein Homogeneous Manifolds by Yu.G. Nikonorov

Atlas home || Conferences | Abstracts | about Atlas

Geometry and Applications
March 13-16, 2000
Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences and Novosibirsk State University
Novosibirsk, Russia

Organizers
Yu.G. Rushetnyak (Chair of Program Committee; Russia), V.V. Vershinin (Chair of Organizing Committee; Russia), A.A. Borisenko (Ukraine), Yu.D. Burago (Russia), V.M. Gol'dshtein (Israel), M.L. Gromov (France), I.G. Nikolaev (USA/Russia), S.P. Novikov (USA/Russia), A.V. Pogorelov (Ukraine), I.Kh. Sabitov (Russia)

View Abstracts
Conference Homepage

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