Displaying similar documents to “On the structure of Riemannian manifolds of almost nonnegative Ricci curvature.”

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

Yana Alexieva, Stefan Ivanov (1999)

Archivum Mathematicum

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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 0 , which are not locally homogeneous, in general.