Clifford-wolf homogeneous riemannian manifolds

Valerii N. Berestovskii Omsk Branch of Sobolev Institute Yurii G. Nikonorov of Altay State Technical University

Differential Geometry mathscidoc:1609.10124

Journal of Differential Geometry, 82, (3), 467-500, 2009
In this paper, using connections between Clifford-Wolf isometries and Killing vector fields of constant length on a given Riemannian manifold, we classify simply connected Clifford-Wolf homogeneous Riemannian manifolds. We also get the classification of complete simply connected Riemannian manifolds with the Killing property defined and studied previously by J.E. D’Atri and H.K. Nickerson. In the last part of the paper we study properties of Clifford-Killing spaces, that is, real vector spaces of Killing vector fields of constant length, on odd-dimensional round spheres,and discuss numerous connections between these spaces and various classical objects.
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  author={Valerii N. Berestovskii, and Yurii G. Nikonorov},
  booktitle={Journal of Differential Geometry},
Valerii N. Berestovskii, and Yurii G. Nikonorov. CLIFFORD-WOLF HOMOGENEOUS RIEMANNIAN MANIFOLDS. 2009. Vol. 82. In Journal of Differential Geometry. pp.467-500.
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