Dokument
| Titel: | On metric connections with totally skew-symmetric torsion tensor |
| Autor: | Vasilev, Stefan |
| Weitere Beteiligte: | Agricola, Ilka (Prof. Dr. habil.) |
| Veröffentlicht: | 2019 |
| URI: | https://archiv.ub.uni-marburg.de/diss/z2020/0088 |
| URN: | urn:nbn:de:hebis:04-z2020-00885 |
| DOI: | https://doi.org/10.17192/z2020.0088 |
| DDC: | 510 Mathematik |
| Titel (trans.): | Über metrische Zusammenhänge mit schief-symmetrischer Torsion |
| Publikationsdatum: | 2020-03-03 |
| Lizenz: | https://creativecommons.org/licenses/by-nc-sa/4.0 |
| Schlagwörter: |
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| Generalized Weitzenböck formula, Zusammenhang <Mathematik>, Metric connections with totally skew torsion, Nabla-Killing and nabla-confor, Laplace-Operator, Laplace operators with torsion, Torsion <Mathematik> |
Summary:
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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