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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 3, Pages 497–514 (Mi smj1856)  

This article is cited in 70 scientific papers (total in 70 papers)

Killing vector fields of constant length on Riemannian manifolds

V. N. Berestovskiia, Yu. G. Nikonorovb

a Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science
b Rubtsovsk Industrial Intitute, Branch of Altai State Technical University
References:
Abstract: We study the nontrivial Killing vector fields of constant length and the corresponding flows on complete smooth Riemannian manifolds. Various examples are constructed of the Killing vector fields of constant length generated by the isometric effective almost free but not free actions of $S^1$ on the Riemannian manifolds close in some sense to symmetric spaces. The latter manifolds include “almost round” odd-dimensional spheres and unit vector bundles over Riemannian manifolds. We obtain some curvature constraints on the Riemannian manifolds admitting nontrivial Killing fields of constant length.
Keywords: Riemannian manifold, Killing vector field, geodesic, Sasaki metric.
Received: 08.12.2006
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 3, Pages 395–407
DOI: https://doi.org/10.1007/s11202-008-0039-3
Bibliographic databases:
UDC: 514.752.7
Language: Russian
Citation: V. N. Berestovskii, Yu. G. Nikonorov, “Killing vector fields of constant length on Riemannian manifolds”, Sibirsk. Mat. Zh., 49:3 (2008), 497–514; Siberian Math. J., 49:3 (2008), 395–407
Citation in format AMSBIB
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\paper Killing vector fields of constant length on Riemannian manifolds
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\pages 497--514
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  • This publication is cited in the following 70 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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