Riemannian Manifold in Which the Skew-Symmetric Curvature Operator has Pointwise Constant Eigenvalues |
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Authors: | Stefan Ivanov Irina Petrova |
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Institution: | (1) University of Sofia, Faculty of Maths. and Inf., bul. James Boucher 5, 1126 Sofia, Bulgario |
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Abstract: | We study manifolds where the natural skew-symmetric curvature operator has pointwise constant eigenvalues. We give a local classification (up to isometry) of such manifolds in dimension 4. In dimension 3, we describe such manifolds up to a classification of three - dimensional Riemannian manifolds with principal Ricci curvatures r1 = r2 = 0, r3- arbitrary. We give examples of such manifolds in all dimensions which do not have constant sectional curvature; these manifolds are not pointwise Osserman manifolds in general. |
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Keywords: | constant eigenvalues of the curvature operator curvature homogeneous spaces pointwise Osserman manifolds |
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