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Mat. Tr., 2003, Volume 6, Number 2, Pages 80–101 (Mi mt93)  

This article is cited in 8 scientific papers (total in 8 papers)

Invariant Einstein Metrics on Three-Locally-Symmetric Spaces

A. M. Lomshakova, Yu. G. Nikonorovb, E. V. Firsovb

a Barnaul State Pedagogical University
b Rubtsovsk Industrial Intitute, Branch of Altai State Technical University

Abstract: We study the problem of existence and the number of invariant Einstein metrics on three-locally-symmetric spaces. We prove that if there are no isomorphic modules in the isotropy decomposition then the number of invariant Einstein metrics (up to isometry and homothety) varies from one to four. Basing on these results, we construct new examples of Einstein metrics.

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

Full text: PDF file (1960 kB)
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English version:
Siberian Advances in Mathematics, 2004, 14:3, 43–62

Bibliographic databases:

UDC: 514.765
Received: 18.04.2002

Citation: A. M. Lomshakov, Yu. G. Nikonorov, E. V. Firsov, “Invariant Einstein Metrics on Three-Locally-Symmetric Spaces”, Mat. Tr., 6:2 (2003), 80–101; Siberian Adv. Math., 14:3 (2004), 43–62

Citation in format AMSBIB
\Bibitem{LomNikFir03}
\by A.~M.~Lomshakov, Yu.~G.~Nikonorov, E.~V.~Firsov
\paper Invariant Einstein Metrics on Three-Locally-Symmetric Spaces
\jour Mat. Tr.
\yr 2003
\vol 6
\issue 2
\pages 80--101
\mathnet{http://mi.mathnet.ru/mt93}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2033648}
\zmath{https://zbmath.org/?q=an:1077.53512|1054.53067}
\transl
\jour Siberian Adv. Math.
\yr 2004
\vol 14
\issue 3
\pages 43--62


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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. Arvanitoyeorgos A., Dzhepko V.V., Nikonorov Yu.G., “Invariant Einstein Metrics on Some Homogeneous Spaces of Classical Lie Groups”, Canadian Journal of Mathematics-Journal Canadien de Mathematiques, 61:6 (2009), 1201–1213  crossref  mathscinet  zmath  isi  scopus
    2. Arvanitoyeorgos A., Chrysikos I., “Invariant Einstein metrics on flag manifolds with four isotropy summands”, Annals of Global Analysis and Geometry, 37:2 (2010), 185–219  crossref  mathscinet  zmath  isi  scopus
    3. Abiev N.A., Arvanitoyeorgos A., Nikonorov Yu.G., Siasos P., “the Dynamics of the Ricci Flow on Generalized Wallach Spaces”, Differ. Geom. Appl., 35:1 (2014), 26–43  crossref  mathscinet  zmath  isi  elib  scopus
    4. Abiev N., “Two-Parametric Bifurcations of Singular Points of the Normalized Ricci Flow on Generalized Wallach Spaces”, AIP Conference Proceedings, 1676, eds. Ashyralyev A., Malkowsky E., Lukashov A., Basar F., Amer Inst Physics, 2015, 020053  crossref  isi  scopus
    5. Nikonorov Yu.G., “Classification of Generalized Wallach Spaces”, Geod. Dedic., 181:1 (2016), 193–212  crossref  mathscinet  zmath  isi  scopus
    6. Abiev N.A., Nikonorov Yu.G., “the Evolution of Positively Curved Invariant Riemannian Metrics on the Wallach Spaces Under the Ricci Flow”, Ann. Glob. Anal. Geom., 50:1 (2016), 65–84  crossref  mathscinet  zmath  isi  scopus
    7. Chen Zh., Kang Y., Liang K., “Invariant Einstein Metrics on Three-Locally-Symmetric Spaces”, Commun. Anal. Geom., 24:4 (2016), 769–792  crossref  mathscinet  zmath  isi
    8. N. A. Abiev, “Ob evolyutsii invariantnykh rimanovykh metrik na odnom klasse obobschennykh prostranstv Uollakha pod vliyaniem normalizovannogo potoka Richchi”, Matem. tr., 20:1 (2017), 3–20  mathnet  crossref  elib
  • Математические труды Siberian Advances in Mathematics
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