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KILLING VECTOR FIELDS OF CONSTANT LENGTH ON LOCALLY SYMMETRIC RIEMANNIAN MANIFOLDS

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Abstract

In this paper nontrivial Killing vector fields of constant length and the corresponding ows on smooth complete Riemannian manifolds are investigated. It is proved that such a ow on symmetric space is free or induced by a free isometric action of the circle S 1. Examples of unit Killing vector fields generated by almost free but not free actions of S 1 on locally symmetric Riemannian spaces are found; among them are homogeneous (nonsimply connected) Riemannian manifolds of constant positive sectional curvature and locally Euclidean spaces. Some unsolved questions are formulated.

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Authors and Affiliations

  1. Omsk Branch of the Sobolev Institute of Mathematics SD RAS, 644099, Omsk ul. Pevtsova, 13, Russia

    V. N. BERESTOVSKIĬ

  2. Rubtsovsk Industrial Institute of Altay State Technical University, 658207, Rubtsovsk ul. Traktornaya, 2/6, Russia

    YU. G. NIKONOROV

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  1. V. N. BERESTOVSKIĬ
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  2. YU. G. NIKONOROV
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Correspondence to V. N. BERESTOVSKIĬ.

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DOI: 10.1007/s00031-008-9000-6.

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BERESTOVSKIĬ, V.N., NIKONOROV, Y.G. KILLING VECTOR FIELDS OF CONSTANT LENGTH ON LOCALLY SYMMETRIC RIEMANNIAN MANIFOLDS. Transformation Groups 13, 25–45 (2008). https://doi.org/10.1007/s00031-008-9000-6

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  • DOI: https://doi.org/10.1007/s00031-008-9000-6

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