Clifford-Wolf homogeneous Riemannian manifolds
Berestovskii, Valerii N. ; Nikonorov, Yurii G.
J. Differential Geom., Tome 81 (2009) no. 2, p. 467-500 / Harvested from Project Euclid
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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.
Publié le : 2009-07-15
Classification:  
@article{1251122544,
     author = {Berestovskii, Valerii N. and Nikonorov, Yurii G.},
     title = {Clifford-Wolf homogeneous Riemannian manifolds},
     journal = {J. Differential Geom.},
     volume = {81},
     number = {2},
     year = {2009},
     pages = { 467-500},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1251122544}
}

Berestovskii, Valerii N.; Nikonorov, Yurii G. Clifford-Wolf homogeneous Riemannian manifolds. J. Differential Geom., Tome 81 (2009) no. 2, pp.  467-500. http://gdmltest.u-ga.fr/item/1251122544/