Abstract
Osserman conjectured that if the curvature operatorR of a Riemannian manifoldM has constant eigenvalues, thenM is locally a rank-1 symmetric space or is flat. The pointwise question is considerably more complicated. We present examples of Riemannian manifolds so thatR has constant eigenvalues at the basepoint, butR is not the curvature operator of a rank-1 symmetric space.
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Research partially supported by the NSF and IHES.
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Gilkey, P.B. Manifolds whose curvature operator has constant eigenvalues at the basepoint. J Geom Anal 4, 155–158 (1994). https://doi.org/10.1007/BF02921544
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DOI: https://doi.org/10.1007/BF02921544