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Mat. Tr., 2009, Volume 12, Number 1, Pages 40–116 (Mi mt175)  

This article is cited in 16 scientific papers (total in 16 papers)

The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The nonunimodular case

A. G. Kremlyov, Yu. G. Nikonorov

Rubtsovsk Industrial Intitute, Rubtsovsk, Russia

Abstract: We obtain a complete classification of all the possible values of the signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional nonunimodular Lie groups.

Key words: homogeneous Riemannian manifold, Lie algebra, Lie group, left-invariant Riemannian metric, Ricci curvature.

Full text: PDF file (535 kB)
References: PDF file   HTML file

English version:
Siberian Advances in Mathematics, 2010, 20:1, 1–57

Bibliographic databases:

UDC: 514.765
Received: 16.07.2008

Citation: A. G. Kremlyov, Yu. G. Nikonorov, “The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The nonunimodular case”, Mat. Tr., 12:1 (2009), 40–116; Siberian Adv. Math., 20:1 (2010), 1–57

Citation in format AMSBIB
\Bibitem{KreNik09}
\by A.~G.~Kremlyov, Yu.~G.~Nikonorov
\paper The signature of the Ricci curvature of left-invariant Riemannian metrics on four-dimensional Lie groups. The nonunimodular case
\jour Mat. Tr.
\yr 2009
\vol 12
\issue 1
\pages 40--116
\mathnet{http://mi.mathnet.ru/mt175}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2569648}
\elib{http://elibrary.ru/item.asp?id=15313337}
\transl
\jour Siberian Adv. Math.
\yr 2010
\vol 20
\issue 1
\pages 1--57
\crossref{https://doi.org/10.3103/S1055134410010013}


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    This publication is cited in the following articles:
    1. M. S. Chebarykov, “On the Ricci curvature of nonunimodular solvable metric Lie algebras of small dimension”, Siberian Adv. Math., 21:2 (2011), 81–99  mathnet  crossref  mathscinet  elib
    2. Voronov D.S., Rodionov E.D., “Left-invariant Riemannian metrics on four-dimensional nonunimodular Lie groups with zero-divergence Weyl tensor”, Dokl. Math., 81:3 (2010), 392–394  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. Gladunova O.P., Rodionov E.D., Slavskii V.V., “Ob operatore krivizny na chetyrekhmernykh gruppakh Li s levoinvariantnoi rimanovoi metrikoi”, Izv. Altaiskogo gos. un-ta, 2010, no. 1-2, 29–33  elib
    4. O. P. Gladunova, E. D. Rodionov, V. V. Slavskii, “O konformno poluploskikh 4-mernykh gruppakh Li”, Vladikavk. matem. zhurn., 13:3 (2011), 3–16  mathnet
    5. Gladunova O.P., Rodionov E.D., Slavskii V.V., “Invariantnye tenzornye polya na gruppakh Li maloi razmernosti”, Vestnik Kemerovskogo gosudarstvennogo universiteta, 2011, no. 3-1, 119–133  mathscinet  elib
    6. D. S. Voronov, O. P. Gladunova, E. D. Rodionov, V. V. Slavskii, “Ob invariantnykh tenzornykh polyakh na gruppakh Li malykh razmernostei”, Vladikavk. matem. zhurn., 14:2 (2012), 3–30  mathnet
    7. Yu. G. Nikonorov, M. S. Chebarykov, “The Ricci operator of completely solvable metric Lie algebras”, Siberian Adv. Math., 24:1 (2014), 18–25  mathnet  crossref  mathscinet  elib
    8. N. A. Abiev, “On the Ricci curvature of solvable metric lie algebras with two-step nilpotent derived algebras”, Siberian Adv. Math., 24:1 (2014), 1–11  mathnet  crossref  mathscinet
    9. M. S. Chebarykov, “O krivizne Richchi trekhmernykh metricheskikh algebr Li”, Vladikavk. matem. zhurn., 16:1 (2014), 57–67  mathnet
    10. Nikonorov Yu.G., “Negative Eigenvalues of the Ricci Operator of Solvable Metric Lie Algebras”, Geod. Dedic., 170:1 (2014), 119–133  crossref  mathscinet  zmath  isi  scopus
    11. Kubo A., Onda K., Taketomi Yu., Tamaru H., “on the Moduli Spaces of Left-Invariant Pseudo-Riemannian Metrics on Lie Groups”, Hiroshima Math. J., 46:3 (2016), 357–374  mathscinet  zmath  isi
    12. Ngaha M.B.D., Boucetta M., Kamga J.W., “the Signature of the Ricci Curvature of Left-Invariant Riemannian Metrics on Nilpotent Lie Groups”, Differ. Geom. Appl., 47 (2016), 26–42  crossref  mathscinet  zmath  isi  scopus
    13. Hashinaga T., Tamaru H., Terada K., “Milnor-Type Theorems For Left-Invariant Riemannian Metrics on Lie Groups”, J. Math. Soc. Jpn., 68:2 (2016), 669–684  crossref  mathscinet  zmath  isi  scopus
    14. Tamaru H., “the Space of Left-Invariant Riemannian Metrics”, Geometry and Topology of Manifolds, Springer Proceedings in Mathematics & Statistics, 154, eds. Futaki A., Miyaoka R., Tang Z., Zhang W., Springer Japan, 2016, 315–326  crossref  mathscinet  zmath  isi  scopus
    15. Boucetta M., Lebzioui H., “Flat Nonunimodular Lorentzian Lie Algebras”, Commun. Algebr., 44:10 (2016), 4185–4195  crossref  mathscinet  zmath  isi  scopus
    16. Cairns G., Galic A.H., Nikolayevsky Yu., “Curvature Properties of Metric Nilpotent Lie Algebras Which Are Independent of Metric”, Ann. Glob. Anal. Geom., 51:3 (2017), 305–325  crossref  mathscinet  zmath  isi  scopus
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