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Sibirsk. Mat. Zh., 2013, Volume 54, Number 5, Pages 972–988 (Mi smj2470)  

This article is cited in 1 scientific paper (total in 1 paper)

Generalized normal homogeneous spheres $S^{4n+3}$ with greatest connected motion group $Sp(n+1)\cdot U(1)$

V. N. Berestovskiĭ

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Omsk, Russia

Abstract: We find all (new) $\delta$-homogeneous invariant Riemannian metrics (including the metrics that are not normal homogeneous) on the spheres of dimensions $4n+3$, $n\ge1$, with the greatest Lie group of isometries equal to $Sp(n+1)\times U(1)$ and all homogeneous (non-simply-connected) lens spaces covered by them. All $\delta$-homogeneous Riemannian spaces considered here have positive sectional curvatures and zero Euler characteristic. The answers are found to some previously posed questions.

Keywords: geodesic orbit space, geodesic vector, $\delta$-homogeneous space, $\delta$-vector, sphere, naturally reductive space, (generalized) normal homogeneous Riemannian space, homogeneous Riemannian fibration, Riemannian submersion, division ring of quaternions, Euler characteristic.

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English version:
Siberian Mathematical Journal, 2013, 54:5, 776–789

Bibliographic databases:

UDC: 514.70
Received: 20.09.2012

Citation: V. N. Berestovskiǐ, “Generalized normal homogeneous spheres $S^{4n+3}$ with greatest connected motion group $Sp(n+1)\cdot U(1)$”, Sibirsk. Mat. Zh., 54:5 (2013), 972–988; Siberian Math. J., 54:5 (2013), 776–789

Citation in format AMSBIB
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\paper Generalized normal homogeneous spheres $S^{4n+3}$ with greatest connected motion group $Sp(n+1)\cdot U(1)$
\jour Sibirsk. Mat. Zh.
\yr 2013
\vol 54
\issue 5
\pages 972--988
\mathnet{http://mi.mathnet.ru/smj2470}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3154795}
\transl
\jour Siberian Math. J.
\yr 2013
\vol 54
\issue 5
\pages 776--789
\crossref{https://doi.org/10.1134/S0037446613050029}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Berestovskii V.N., Nikonorov Yu.G., “Generalized Normal Homogeneous Riemannian Metrics on Spheres and Projective Spaces”, Ann. Glob. Anal. Geom., 45:3 (2014), 167–196  crossref  mathscinet  zmath  isi  elib  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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