On metric connections with totally skew-symmetric torsion tensor

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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Автор: Vasilev, Stefan
Інші автори: Agricola, Ilka (Prof. Dr. habil.) (Керівник дипломної роботи)
Формат: Dissertation
Мова:англійська
Опубліковано: Philipps-Universität Marburg 2019
Предмети:
Generalized Weitzenböck formula
Mathematik
Zusammenhang <Mathematik>
Metric connections with totally skew torsion
Nabla-Killing and nabla-confor
Laplace-Operator
Laplace operators with torsion
Torsion <Mathematik>
Mathematics
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Резюме: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.
Фізичний опис:77 Seiten
DOI:10.17192/z2020.0088

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