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Riemannian manifolds in which certain curvature operator has constant eigenvalues along each helix

Yana Alexieva; Stefan Ivanov — 1999

Archivum Mathematicum

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 $r_{1} = r_{2} = 0, r_{3} \neq 0$ , which are not locally homogeneous, in general.

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