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 Sibirsk. Mat. Zh., 2008, Volume 49, Number 3, Pages 497–514 (Mi smj1856)

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

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.

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English version:
Siberian Mathematical Journal, 2008, 49:3, 395–407

Bibliographic databases:

UDC: 514.752.7

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
\Bibitem{BerNik08} \by V.~N.~Berestovskii, Yu.~G.~Nikonorov \paper Killing vector fields of constant length on Riemannian manifolds \jour Sibirsk. Mat. Zh. \yr 2008 \vol 49 \issue 3 \pages 497--514 \mathnet{http://mi.mathnet.ru/smj1856} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2442533} \zmath{https://zbmath.org/?q=an:1164.53346} \transl \jour Siberian Math. J. \yr 2008 \vol 49 \issue 3 \pages 395--407 \crossref{https://doi.org/10.1007/s11202-008-0039-3} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000256329000003} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-44349172865} 

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