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Vladikavkaz. Mat. Zh., 2013, Volume 15, Number 3, Pages 67–76 (Mi vmj473)  

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

Geodesic orbit Riemannian metrics on spheres

Yu. G. Nikonorov

South Mathematical Institute of VSC RAS, Vladikavkaz, Markus str., 22, 362027, Russia

Abstract: In this paper, a complete classification of geodesic orbit Riemannian metrics on spheres $S^n$ is obtained. We also construct some explicit examples of geodesic vectors for $Sp(n+1)U(1)$-invariant metrics on $S^{4n+3}$.

Key words: homogeneous spaces, homogeneous Riemannian manifolds, naturally reductive Riemannian manifolds, normal homogeneous Riemannian manifolds, geodesic orbit spaces, symmetric spaces, weakly symmetric spaces.

Full text: PDF file (187 kB)
References: PDF file   HTML file
UDC: 514.765
MSC: Primary 53C20; Secondary 53C25, 53C35
Received: 06.11.2012
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Citation: Yu. G. Nikonorov, “Geodesic orbit Riemannian metrics on spheres”, Vladikavkaz. Mat. Zh., 15:3 (2013), 67–76

Citation in format AMSBIB
\Bibitem{Nik13}
\by Yu.~G.~Nikonorov
\paper Geodesic orbit Riemannian metrics on spheres
\jour Vladikavkaz. Mat. Zh.
\yr 2013
\vol 15
\issue 3
\pages 67--76
\mathnet{http://mi.mathnet.ru/vmj473}


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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. Souris N.P., “on a Class of Geodesic Orbit Spaces With Abelian Isotropy Subgroup”, Manuscr. Math.  crossref  isi  scopus
    2. V. N. Berestovskiǐ, “Generalized normal homogeneous spheres”, Siberian Math. J., 54:4 (2013), 588–603  mathnet  crossref  mathscinet  isi
    3. Yu. G. Nikonorov, “On the structure of geodesic orbit Riemannian spaces”, Ann. Glob. Anal. Geom., 52:3 (2017), 289–311  crossref  mathscinet  zmath  isi  scopus
    4. M. Xu, “Geodesic orbit spheres and constant curvature in Finsler geometry”, Differ. Geom. Appl., 61 (2018), 197–206  crossref  mathscinet  zmath  isi  scopus
    5. C. S. Gordon, Yu. G. Nikonorov, “Geodesic orbit Riemannian structures on $\mathbf{R}^n$”, J. Geom. Phys., 134 (2018), 235–243  crossref  mathscinet  zmath  isi  scopus
    6. N. P. Souris, “Geodesic orbit metrics in compact homogeneous manifolds with equivalent isotropy submodules”, Transform. Groups, 23:4 (2018), 1149–1165  crossref  mathscinet  zmath  isi  scopus
    7. H. Chen, Zh. Chen, J. A. Wolf, “Geodesic orbit metrics on compact simple Lie groups arising from flag manifolds”, C. R. Math., 356:8 (2018), 846–851  crossref  mathscinet  zmath  isi  scopus
    8. Z. Dusek, “Homogeneous geodesics and g.o. manifolds”, Note Mat., 38:1 (2018), 1–15  crossref  mathscinet  isi  scopus
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