Abstract.
We characterize Osserman and conformally Osserman Riemannian manifolds with the local structure of a warped product. By means of this approach we analyze the twisted product structure and obtain, as a consequence, that the only Osserman manifolds which can be written as a twisted product are those of constant curvature. Pseudo-Riemannian versions of those results are also considered, showing that four-dimensional conformally Osserman warped products are locally conformally flat. The result however fails in higher dimensions where there exist conformally Osserman products which are not locally conformally flat.
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Dedicated to Udo Simon on the occasion of his 70th birthday
Supported by projects MTM2006-01432 and PGIDIT06PXIB207054PR (Spain).
Received: May 26, 2008. Revised: July 7, 2008.
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Brozos-Vázquez, M., García-Río, E. & Vázquez-Lorenzo, R. Osserman and Conformally Osserman Manifolds with Warped and Twisted Product Structure. Result. Math. 52, 211–221 (2008). https://doi.org/10.1007/s00025-008-0306-4
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DOI: https://doi.org/10.1007/s00025-008-0306-4