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Mat. Tr., 2005, Volume 8, Number 1, Pages 71–121 (Mi mt56)  

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

Six-Dimensional Einstein Solvmanifolds

E. V. Nikitenko, Yu. G. Nikonorov

Rubtsovsk Industrial Intitute, Branch of Altai State Technical University

Abstract: In this article, we completely classify the six-dimensional Einstein solvmanifolds. In particular, we show that all such solvmanifolds are standard. We also classify the homogeneous Einstein 6-manifolds of nonpositive sectional curvature. Moreover, we obtain some structural results about several classes of Einstein solvmanifolds of greater dimension.

Key words: Riemannian manifold, solvmanifold, homogeneous space, Einstein metric.

Full text: PDF file (4247 kB)
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English version:
Siberian Advances in Mathematics, 2006, 16:1, 66–112

Bibliographic databases:

UDC: 514.765
Received: 25.06.2004

Citation: E. V. Nikitenko, Yu. G. Nikonorov, “Six-Dimensional Einstein Solvmanifolds”, Mat. Tr., 8:1 (2005), 71–121; Siberian Adv. Math., 16:1 (2006), 66–112

Citation in format AMSBIB
\Bibitem{NikNik05}
\by E.~V.~Nikitenko, Yu.~G.~Nikonorov
\paper Six-Dimensional Einstein Solvmanifolds
\jour Mat. Tr.
\yr 2005
\vol 8
\issue 1
\pages 71--121
\mathnet{http://mi.mathnet.ru/mt56}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1955023}
\elib{http://elibrary.ru/item.asp?id=9535715}
\transl
\jour Siberian Adv. Math.
\yr 2006
\vol 16
\issue 1
\pages 66--112


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. V. Nikitenko, “Seven-Dimensional Homogeneous Einstein Manifolds\break of Negative Sectional Curvature”, Siberian Adv. Math., 16:3 (2006), 99–114  mathnet  mathscinet  elib
    2. E. V. Nikitenko, “O nestandartnykh einshteinovykh rasshireniyakh pyatimernykh metricheskikh nilpotentnykh algebr Li”, Sib. elektron. matem. izv., 3 (2006), 115–136  mathnet  mathscinet  zmath
    3. Yu. G. Nikonorov, “On Einstein Extensions of Nilpotent Metric Lie Algebras”, Siberian Adv. Math., 17:3 (2007), 153–170  mathnet  crossref  mathscinet  elib
    4. 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”, Siberian Adv. Math., 20:1 (2010), 1–57  mathnet  crossref  mathscinet  elib
    5. Lauret J., “Einstein solvmanifolds and nilsolitons”, New Developments in Lie Theory and Geometry, Contemporary Mathematics, 491, 2009, 1–35  crossref  mathscinet  zmath  isi
    6. 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
    7. Lauret J., “Einstein solvmanifolds are standard”, Ann. of Math. (2), 172:3 (2010), 1859–1877  crossref  mathscinet  zmath  isi  scopus
    8. 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
    9. 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
    10. M. S. Chebarykov, “O krivizne Richchi trekhmernykh metricheskikh algebr Li”, Vladikavk. matem. zhurn., 16:1 (2014), 57–67  mathnet
    11. Lafuente R., Lauret J., “Structure of Homogeneous Ricci Solitons and the Alekseevskii Conjecture”, J. Differ. Geom., 98:2 (2014), 315–347  crossref  mathscinet  zmath  isi  elib
    12. 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
    13. Nikolayevsky Y., Nikonorov Yu.G., “on Solvable Lie Groups of Negative Ricci Curvature”, Math. Z., 280:1-2 (2015), 1–16  crossref  mathscinet  zmath  isi  scopus
    14. Raffero A., “Half-Flat Structures Inducing Einstein Metrics on Homogeneous Spaces”, Ann. Glob. Anal. Geom., 48:1 (2015), 57–73  crossref  mathscinet  zmath  isi  scopus
    15. Nikolayevsky Y., “Solvable Extensions of Negative Ricci Curvature of Filiform Lie Groups”, Math. Nachr., 289:2-3 (2016), 321–331  crossref  mathscinet  zmath  isi  elib  scopus
    16. Arroyo R.M., Lafuente R.A., “the Alekseevskii Conjecture in Low Dimensions”, Math. Ann., 367:1-2 (2017), 283–309  crossref  mathscinet  zmath  isi  scopus
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