Compact locally homogeneous manifolds with parallel Weyl tensor
From MaRDI portal
Publication:6510394
arXiv2306.01600MaRDI QIDQ6510394
Abstract: We construct new examples of compact ECS manifolds, that is, of pseudo-Riemannian manifolds with parallel Weyl tensor that are neither conformally flat nor locally symmetric. Every ECS manifold has rank 1 or 2, the rank being the dimension of a distinguished null parallel distribution discovered by Olszak. Previously known examples of compact ECS manifolds, in every dimension greater than 4, were all of rank 1, geodesically complete, and none of them locally homogeneous. By contrast, our new examples -- all of them geodesically incomplete -- realizing all odd dimensions starting from 5, are still of rank 1, but this time locally homogeneous.
This page was built for publication: Compact locally homogeneous manifolds with parallel Weyl tensor
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6510394)
