Compact pseudo-Riemannian manifolds with parallel Weyl tensor |
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Authors: | Andrzej Derdzinski Witold Roter |
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Affiliation: | 1.Department of Mathematics,The Ohio State University,Columbus,USA;2.Institute of Mathematics and Computer Science,Wroc?aw University of Technology,Wroc?aw,Poland |
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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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