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Compact pseudo-Riemannian manifolds with parallel Weyl tensor

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Abstract

It is shown that in every dimension n = 3j + 2, j = 1, 2, 3, . . ., there exist compact pseudo-Riemannian manifolds with parallel Weyl tensor, which are Ricci-recurrent, but neither conformally flat nor locally symmetric, and represent all indefinite metric signatures. The manifolds in question are diffeomorphic to nontrivial torus bundles over the circle. They all arise from a construction that a priori yields bundles over the circle, having as the fibre either a torus, or a 2-step nilmanifold with a complete flat torsionfree connection; our argument only realizes the torus case.

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Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, Columbus, OH, 43210, USA

    Andrzej Derdzinski

  2. Institute of Mathematics and Computer Science, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Witold Roter

Authors
  1. Andrzej Derdzinski
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  2. Witold Roter
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Correspondence to Andrzej Derdzinski.

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Derdzinski, A., Roter, W. Compact pseudo-Riemannian manifolds with parallel Weyl tensor. Ann Glob Anal Geom 37, 73–90 (2010). https://doi.org/10.1007/s10455-009-9173-9

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  • DOI: https://doi.org/10.1007/s10455-009-9173-9

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