Geodesic
On the Ricci curvature of solvable metric lie algebras with two-step nilpotent derived algebras
Matematičeskie trudy, Tome 16 (2013) no. 1, pp. 3-17.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that the Ricci operator of any nonunimoular solvable metric Lie algebra having a two-step nilpotent derived Lie algebra of dimension 6 has at least two negative eigenvalues. 
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N. A. Abiev. On the Ricci curvature of solvable metric lie algebras with two-step nilpotent derived algebras. Matematičeskie trudy, Tome 16 (2013) no. 1, pp. 3-17. http://geodesic.mathdoc.fr/item/MT_2013_16_1_a0/

[1] Alekseevskii D. V., “Odnorodnye rimanovy prostranstva otritsatelnoi krivizny”, Matem. sb., 96(138):1 (1975), 93–117 | MR | Zbl

[2] Besse A. L., Mnogoobraziya Einshteina, Mir, M., 1990 | MR | Zbl

[3] Kremlev A. G., Nikonorov Yu. G., “Signatura krivizny Richchi levoinvariantnykh rimanovykh metrik na chetyrekhmernykh gruppakh Li. Unimodulyarnyi sluchai”, Matem. tr., 11:2 (2008), 115–147 | MR | Zbl

[4] Kremlev A. G., Nikonorov Yu. G., “Signatura krivizny Richchi levoinvariantnykh rimanovykh metrik na chetyrekhmernykh gruppakh Li. Neunimodulyarnyi sluchai”, Matem. tr., 12:1 (2009), 40–116 | MR | Zbl

[5] Morozov V. V., “Klassifikatsiya nilpotentnykh algebr Li shestogo poryadka”, Izv. vuzov. Matem., 1958, no. 4(5), 161–171 | MR | Zbl

[6] Nikitenko E. V., “O nestandartnykh einshteinovykh rasshireniyakh pyatimernykh metricheskikh nilpotentnykh algebr Li”, Sib. elektron. matem. izv., 3 (2006), 115–136 | MR | Zbl

[7] Nikitenko E. V., Nikonorov Yu. G., “Shestimernye einshteinovy solvmnogoobraziya”, Matem. tr., 8:1 (2005), 71–121 | MR | Zbl

[8] Nikonorov Yu. G., Chebarykov M. S., “Operator Richchi vpolne razreshimykh metricheskikh algebr Li”, Matem. tr., 15:2 (2012), 146–158 | MR

[9] Chebarykov M. S., “O krivizne Richchi neunimodulyarnykh razreshimykh metricheskikh algebr Li maloi razmernosti”, Matem. tr., 13:1 (2010), 186–211 | MR | Zbl

[10] Console S., Fino A., Samiou E., “The moduli space of six\@dimensional two\@step nilpotent Lie algebras”, Ann. Global Anal. Geom., 27:1 (2005), 17–32 | DOI | MR | Zbl

[11] Eberlein P., “Geometry of 2-step nilpotent Lie groups”, Modern Dynamical Systems and Applications, Cambridge Univ. Press, Cambridge, 2004, 67–101 | MR | Zbl

[12] De Graaf W. A., “Classification of 6-dimensional nilpotent Lie algebras over field of characteristic not 2”, J. Algebra, 309:2 (2007), 640–653 | DOI | MR | Zbl

[13] Milnor J., “Curvatures of left-invariant metrics on Lie groups”, Adv. Math, 21:3 (1976), 293–329 | DOI | MR | Zbl

[14] Patera J., Sharp R. T., Winternitz P., Zassenhaus H., “Invariants of real low dimension Lie algebras”, J. Mathematical Phys., 17:6 (1976), 986–994 | DOI | MR | Zbl

[15] Will C., “Rank-one Einstein solvmanifolds of dimension 7”, Differential Geom. Appl., 19:3 (2003), 307–318 | DOI | MR | Zbl