Address. University of Sofia, Faculty of Mathematics and Informatics, Department of Geometry, bul. James Borchier 5, 1164 Sofia, BULGARIA
Abstract. 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 $r_1 = r_2 = 0, r_3 \not =0$, which are not locally homogeneous, in general.
AMSclassification. 53C15, 53C55, 53B35
Keywords. Helix, constant eigenvalues of the curvature operator, locally symmetric spaces, curvature homogeneous spaces