- Path:
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Compact locally homogeneous manifolds with parallel Weyl tensor
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Periodical
- Title:
- Advances in geometry
- Publication:
-
Berlin [u.a.]: de Gruyter, 2001 -
- Scope:
- Online-Ressource
- Note:
- Gesehen am 26.06.20
- ISSN:
- 1615-7168
- ZDB-ID:
-
2043066-8
- Keywords:
- Geometrie ; Zeitschrift
- Classification:
- Mathematik
- DDC Group:
- 500 Naturwissenschaften
- Copyright:
- Rights reserved
- Accessibility:
- Eingeschränkter Zugang mit Nutzungsbeschränkungen
- Collection:
- Mathematik
Article
- Title:
- Compact locally homogeneous manifolds with parallel Weyl tensor
- Publication:
-
Berlin [u.a.]: de Gruyter, 2024
- Language:
- English
- Scope:
- Online-Ressource
- Note:
- Kein Open Access
- Archivierung/Langzeitarchivierung gewährleistet
- Keywords:
- Parallel Weyl tensor ; conformally symmetric manifold ; compact pseudo-Riemannian manifold ; Primary 53C50
- Classification:
- Mathematik
- Sonstiges
- Collection:
- Mathematik
- Sonstiges
- Copyright:
- Rights reserved
- Accessibility:
- Eingeschränkter Zugang mit Nutzungsbeschränkungen
- Information:
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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 was locally homogeneous. In contrast, our new examples — all of them geodesically incomplete — realize all odd dimensions starting from 5 and are of rank 2, as well as locally homogeneous.
