Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix
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 , which are not locally homogeneous, in general.