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arXiv · 2210.03660

New examples of compact Weyl-parallel manifolds

Andrzej Derdzinski·Ivo Terek
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Abstract

We prove the existence of compact pseudo-Riemannian manifolds with parallel Weyl tensor which are neither conformally flat nor locally symmetric, and represent all indefinite metric signatures in all dimensions $\,n\ge5$. Until now such manifolds were only known to exist in dimensions $\,n=3j+2$, where $\,j\,$ is any positive integer [11]. As in [11], our examples are diffeomorphic to nontrivial torus bundles over the circle and arise from a quotient-manifold construction applied to suitably chosen discrete isometry groups of diffeomorphically-Euclidean "model" manifolds.

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Andrzej Derdzinski, Ivo Terek. 2022-10-07. New examples of compact Weyl-parallel manifolds. https://doi.org/10.1007/s00605-023-01908-0

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