Geodesic
On the Ricci curvature of nonunimodular solvable metric Lie algebras of small dimension
Matematičeskie trudy, Tome 13 (2010) no. 1, pp. 186-211 Cet article a éte moissonné depuis la source Math-Net.Ru

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The Ricci curvature of solvable metric Lie algebras is studied. In particular, we prove that the Ricci operator of any metric nonunimodular solvable Lie algebra of dimension not exceeding 6 has at least two negative eigenvalues, that generalizes the known results. 
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M. S. Chebarykov. On the Ricci curvature of nonunimodular solvable metric Lie algebras of small dimension. Matematičeskie trudy, Tome 13 (2010) no. 1, pp. 186-211. http://geodesic.mathdoc.fr/item/MT_2010_13_1_a8/

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

[2] Alekseevskii D. V., Kimelfeld B. N., “Struktura odnorodnykh rimanovykh prostranstv s nulevoi kriviznoi Richchi”, Funktsion. analiz i ego pril., 9:2 (1975), 5–11 | MR | Zbl

[3] Balaschenko V. V., Nikonorov Yu. G., Rodionov E. D., Slavskii V. V., Odnorodnye prostranstva: teoriya i prilozheniya, Poligrafist, Khanty-Mansiisk, 2008

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

[5] Burbaki N., Gruppy i algebry Li, Mir, M., 1978 | MR

[6] Vinberg E. B., Gorbatsevich V. V., Onischik A. L., “Stroenie grupp i algebr Li”, Itogi nauki i tekhniki. Sovremennye problemy matematiki. Fundamentalnye napravleniya, 41, VINITI, M., 1990, 5–253 | MR | Zbl

[7] Gantmakher F. R., Teoriya matrits, Nauka, M., 1988 | MR | Zbl

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

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

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

[11] Mubarakzyanov G. M., “O razreshimykh algebrakh Li”, Izv. vuzov. Matematika, 1963, no. 1(32), 114–123 | MR | Zbl

[12] Mubarakzyanov G. M., “Klassifikatsiya veschestvennykh struktur algebr Li pyatogo poryadka”, Izv. vuzov. Matematika, 1963, no. 3(34), 99–106 | MR | Zbl

[13] Nikitenko E. V., “O nestandartnykh einshteinovykh rasshireniyakh pyatimernykh metricheskikh nilpotentnykh algebr Li”, Sibirskie elektronnye matematicheskie izvestiya, 3, 2006, 115–136 | MR | Zbl

[14] Nikitenko E. V., Nikonorov Yu. G., “Shestimernye einshteinovy solvmnogoobraziya”, Mat. trudy, 8:1 (2005), 71–121 | MR

[15] Nikonorov Yu. G., Rodionov E. D., Slavskii V. V., “Geometriya odnorodnykh rimanovykh mnogoobrazii”, Sovremennaya matematika i ee prilozheniya, 37, Geometriya (2006), 101–178 | MR

[16] Khorn R., Dzhonson Ch., Matrichnyi analiz, Mir, M., 1989 | MR

[17] De Graaf W. A., “Classification of solvable Lie algebras”, Experiment. Math., 14:1 (2005), 15–25 | MR | Zbl

[18] Dotti Miatello I., “Ricci curvature of left-invariant metrics on solvable unimodular Lie groups”, Math. Z., 180:2 (1982), 257–263 | MR | Zbl

[19] Jacobson N., Lie Algebras, Interscience Tracts in Pure and Applied Mathematics, 10, Interscience Publishers, New York, 1962 | MR | Zbl

[20] Jensen G., “The scalar curvature of left-invariant Riemannian metrics”, Indiana Univ. Math. J., 20 (1971), 1125–1143 | DOI | MR

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

[22] 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