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Riemannian Manifolds in Which Certain Curvature Operator Has Constant Eigenvalues along Each Circle

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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 r 1 = r 2 = 0, r 3= 0 , which are not locally homogeneous, in general.

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Authors and Affiliations

  1. Department of Geometry, University of Sofia, bul. James Bouchier 5, 1126, Sofia, Bulgaria

    Stefan Ivanov (Faculty of Mathematics and Informatics) & Irina Petrova

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  1. Stefan Ivanov
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  2. Irina Petrova
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Ivanov, S., Petrova, I. Riemannian Manifolds in Which Certain Curvature Operator Has Constant Eigenvalues along Each Circle. Annals of Global Analysis and Geometry 15, 157–171 (1997). https://doi.org/10.1023/A:1006548328030

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  • DOI: https://doi.org/10.1023/A:1006548328030

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