Riemannian manifolds for which a natural skew-symmetric curvature operator has constant eigenvalues on helices are studied. A local classification in dimension three is given. In the three dimensional case one gets all locally symmetric spaces and all Riemannian manifolds with the constant principal Ricci curvatures $r_1 = r_2 = 0, r_3 \ne 0$, which are not locally homogeneous, in general.
@article{107689,
author = {Yana Alexieva and Stefan Ivanov},
title = {Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix},
journal = {Archivum Mathematicum},
volume = {035},
year = {1999},
pages = {129-140},
zbl = {1054.53058},
mrnumber = {1711665},
language = {en},
url = {http://dml.mathdoc.fr/item/107689}
}
Alexieva, Yana; Ivanov, Stefan. Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix. Archivum Mathematicum, Tome 035 (1999) pp. 129-140. http://gdmltest.u-ga.fr/item/107689/
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