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On metric connections with totally skew-symmetric torsion tensor
We consider a 1-parameter family of metric connections with totally skew-symmetric torsion tensors on a Riemannian manifold and derive a Weitzenböck formula for the Laplace operator, arising from such a connection. Various notions related to the family are defined and developed in the process, mimic...
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| Format: | Dissertation |
| Langue: | anglais |
| Publié: |
Philipps-Universität Marburg
2019
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| Accès en ligne: | Texte intégral en PDF |
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| Résumé: | We consider a 1-parameter family of metric connections with totally skew-symmetric torsion tensors on a Riemannian manifold and derive a Weitzenböck formula for the Laplace operator, arising from such a connection. Various notions related to the family are defined and developed in the process, mimicking what is normally done with the Levi-Civita connection. We investigate the matter of skew torsion further by introducing weakly non-degenerate and non-degenerate split torsion and show examples of manifolds, admitting such connections. |
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| Description matérielle: | 77 Seiten |
| DOI: | 10.17192/z2020.0088 |