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Keywords:
helix; constant eigenvalues of the curvature operator; locally symmetric spaces; curvature homogeneous spaces
helix; constant eigenvalues of the curvature operator; locally symmetric spaces; curvature homogeneous spaces
Summary:
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.
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