Differential Geometry
Einstein solvmanifolds and graphs
Comptes Rendus. Mathématique, Volume 344 (2007) no. 1, pp. 37-39.

In this Note, we obtain Einstein solvmanifolds using Abelian extension of two-step nilpotent Lie algebras associated with graphs.

Dans cette Note, nous obtenons des solvariétés d'Einstein par extension abélienne des algèbres de Lie nilpotentes de rang deux associées à des graphes.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.11.010
Fanaï, Hamid-Reza 1, 2

1 Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11365-9415, Tehran, Iran
2 Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran
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Fanaï, Hamid-Reza. Einstein solvmanifolds and graphs. Comptes Rendus. Mathématique, Volume 344 (2007) no. 1, pp. 37-39. doi : 10.1016/j.crma.2006.11.010. http://www.numdam.org/articles/10.1016/j.crma.2006.11.010/

[1] Alekseevskii, D.V. Classification of quaternionic spaces with a transitive solvable group of motions, Math. USSR-Izv., Volume 9 (1975), pp. 297-339

[2] Dani, S.G.; Mainkar, M.G. Anosov automorphisms on compact nilmanifolds associated with graphs, Trans. Amer. Math. Soc., Volume 357 (2005), pp. 2235-2251

[3] Fanaï, H.-R. Espaces homogènes d'Einstein non-compacts, Geom. Dedicata, Volume 80 (2000), pp. 187-200

[4] Gordon, C.S.; Kerr, M.M. New homogeneous Einstein metrics of negative Ricci curvature, Ann. Global Anal. Geom., Volume 19 (2001), pp. 75-101

[5] Heber, J. Noncompact homogeneous Einstein spaces, Invent. Math., Volume 133 (1998), pp. 279-352

[6] D. Kass-Hengesch, Exemples de variétés homogènes d'Einstein à courbure scalaire négative, Thèse de Doctorat, Université Henri Poincaré-Nancy I, France, 1996

[7] Lanzendorf, M. Einstein metrics with nonpositive sectional curvature on extensions of Lie algebra of Heisenberg type, Geom. Dedicata, Volume 66 (1997), pp. 187-202

[8] Wolter, T. Einstein metrics on solvable groups, Math. Z., Volume 206 (1991), pp. 457-471

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