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Abstract: In this paper, using connections between Clifford-Wolf isometries and Killingvector fields of constant length on a given Riemannian manifold, we classifysimply connected Clifford-Wolf homogeneous Riemannian manifolds. We also getthe classification of complete simply connected Riemannian manifolds with theKilling property defined and studied previously by J.E. D-Atri and H.K.Nickerson. In the last part of the paper we study properties ofClifford-Killing spaces, that is, real vector spaces of Killing vector fieldsof constant length, on odd-dimensional round spheres, and discuss numerousconnections between these spaces and various classical objects.

Author: V.N. Berestovskii Omsk Branch of Sobolev Institute of Mathematics SD RAS, Yu.G. Nikonorov Rubtsovsk Industrial Institute


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