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Mat. Sb., 2004, Volume 195, Number 4, Pages 143–160 (Mi msb817)  

This article is cited in 25 scientific papers (total in 25 papers)

Weakly symmetric Riemannian manifolds with reductive isometry group

O. S. Yakimova

M. V. Lomonosov Moscow State University

Abstract: A classification of non-symmetric weakly symmetric Riemannian manifolds with reductive symmetry group is obtained. In particular, all compact weakly symmetric Riemannian manifolds are described. Many new examples of weakly symmetric manifolds are constructed.


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English version:
Sbornik: Mathematics, 2004, 195:4, 599–614

Bibliographic databases:

UDC: 512.816
MSC: Primary 53C35, 53C30; Secondary 20Gxx
Received: 15.11.2002

Citation: O. S. Yakimova, “Weakly symmetric Riemannian manifolds with reductive isometry group”, Mat. Sb., 195:4 (2004), 143–160; Sb. Math., 195:4 (2004), 599–614

Citation in format AMSBIB
\by O.~S.~Yakimova
\paper Weakly symmetric Riemannian manifolds with reductive isometry group
\jour Mat. Sb.
\yr 2004
\vol 195
\issue 4
\pages 143--160
\jour Sb. Math.
\yr 2004
\vol 195
\issue 4
\pages 599--614

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    This publication is cited in the following articles:
    1. Dmitrii V. Alekseevskii, Yurii G. Nikonorov, “Compact Riemannian Manifolds with Homogeneous Geodesics”, SIGMA, 5 (2009), 093, 16 pp.  mathnet  crossref  mathscinet
    2. Wolf J.A., “Infinite Dimensional Multiplicity Free Spaces II: Limits of Commutative Nilmanifolds”, New Developments in Lie Theory and Geometry, Contemporary Mathematics, 491, 2009, 179–208  crossref  mathscinet  zmath  isi
    3. Deng Sh, “An Algebraic Approach to Weakly Symmetric Finsler Spaces”, Canadian Journal of Mathematics-Journal Canadien de Mathematiques, 62:1 (2010), 52–73  crossref  mathscinet  zmath  isi
    4. Shaoqiang Deng, “Invariant Finsler metrics on polar homogeneous spaces”, Pacific J Math, 247:1 (2010), 47  crossref  mathscinet  zmath  isi
    5. Deng Sh., Hou Z., “Weakly Symmetric Finsler Spaces”, Communications in Contemporary Mathematics, 12:2 (2010), 309–323  crossref  mathscinet  zmath  isi  elib
    6. Shaoqiang Deng, “On the classification of weakly symmetric Finsler spaces”, Isr. J. Math, 181:1 (2011), 29  crossref  mathscinet  zmath  isi
    7. Jovanovic B., “Geodesic Flows on Riemannian g.o. Spaces”, Regular & Chaotic Dynamics, 16:5 (2011), 504–513  crossref  mathscinet  zmath  adsnasa  isi
    8. Wolf J.A., “Infinite dimensional multiplicity free spaces III: matrix coefficients and regular functions”, Math Ann, 349:2 (2011), 263–299  crossref  mathscinet  zmath  isi  elib
    9. V. N. Berestovskiǐ, “Homogeneous almost normal Riemannian manifolds”, Siberian Adv. Math., 24:1 (2014), 12–17  mathnet  crossref  mathscinet
    10. V. N. Berestovskiǐ, “Generalized normal homogeneous spheres $S^{4n+3}$ with greatest connected motion group $Sp(n+1)\cdot U(1)$”, Siberian Math. J., 54:5 (2013), 776–789  mathnet  crossref  mathscinet  isi
    11. Yu. G. Nikonorov, “Geodesic orbit Riemannian metrics on spheres”, Vladikavk. matem. zhurn., 15:3 (2013), 67–76  mathnet
    12. Deng Sh., “On the Symmetry of Riemannian Manifolds”, J. Reine Angew. Math., 680 (2013), 235–256  crossref  mathscinet  zmath  isi  elib
    13. V. N. Berestovskii, V. V. Gorbatsevich, “Homogeneous spaces with inner metric and with integrable invariant distributions”, Anal. Math. Phys., 4:4 (2014), 263–331  crossref  mathscinet  zmath  isi
    14. V. N. Berestovskiǐ, I. A. Zubareva, “Geodesics and shortest arcs of a special sub-Riemannian metric on the Lie group $SL(2)$”, Siberian Math. J., 57:3 (2016), 411–424  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    15. Deng Sh., Matveev V.S., “Locally 2-Fold Symmetric Manifolds Are Locally Symmetric”, Arch. Math., 108:5 (2017), 521–525  crossref  mathscinet  zmath  isi  elib  scopus
    16. Nikonorov Yu.G., “on the Structure of Geodesic Orbit Riemannian Spaces”, Ann. Glob. Anal. Geom., 52:3 (2017), 289–311  crossref  mathscinet  zmath  isi  scopus
    17. Xu M., “Geodesic Orbit Spheres and Constant Curvature in Finsler Geometry”, Differ. Geom. Appl., 61 (2018), 197–206  crossref  mathscinet  zmath  isi  scopus
    18. Souris N.P., “Geodesic Orbit Metrics in Compact Homogeneous Manifolds With Equivalent Isotropy Submodules”, Transform. Groups, 23:4 (2018), 1149–1165  crossref  mathscinet  zmath  isi  scopus
    19. Gordon C.S., Nikonorov Yu.G., “Geodesic Orbit Riemannian Structures on R-N”, J. Geom. Phys., 134 (2018), 235–243  crossref  mathscinet  zmath  isi  scopus
    20. Chen Zh., Wolf J.A., “Semisimple Weakly Symmetric Pseudo-Riemannian Manifolds”, Abh. Math. Semin. Univ. Hamburg, 88:2 (2018), 331–369  crossref  mathscinet  zmath  isi  scopus
    21. Berestovskii V.N. Nikonorov Yu.G., “On Homogeneous Geodesics and Weakly Symmetric Spaces”, Ann. Glob. Anal. Geom., 55:3 (2019), 575–589  crossref  mathscinet  zmath  isi  scopus
    22. Nikonorov Yu.G., “On Left-Invariant Einstein Riemannian Metrics That Are Not Geodesic Orbit”, Transform. Groups, 24:2 (2019), 511–530  crossref  mathscinet  zmath  isi
    23. Zhang B., Chen Zh., Deng Sh., “Pseudo-Riemannian Weakly Symmetric Manifolds of Low Dimension”, Czech. Math. J., 69:3 (2019), 811–835  crossref  mathscinet  zmath  isi
    24. Nikonorov Yu.G., “Spectral Properties of Killing Vector Fields of Constant Length”, J. Geom. Phys., 145 (2019), UNSP 103485  crossref  mathscinet  isi
    25. Chen Zh., Nikonorov Yu., “Geodesic Orbit Riemannian Spaces With Two Isotropy Summands. i”, Geod. Dedic., 203:1 (2019), 163–178  crossref  mathscinet  zmath  isi
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