Riemannian Manifolds in Which Certain Curvature Operator Has Constant Eigenvalues along Each Circle |
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| Authors: | Stefan Ivanov Irina Petrova |
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| Affiliation: | (1) Department of Geometry, University of Sofia, bul. James Bouchier 5, 1126 Sofia, Bulgaria |
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| Abstract: | Riemannian manifolds for which a natural curvature operator has constant eigenvalues on circles are studied. A local classification in dimensions two and three is given. In the 3-dimensional case one gets all locally symmetric spaces and all Riemannian manifolds with the constant principal Ricci curvatures r1 = r2 = 0, r3= 0 , which are not locally homogeneous, in general. |
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| Keywords: | circles constant eigenvalues of the curvature operator curvature homogeneous spaces locally symmetric spaces |
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