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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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Bibliographic Details
Main Author: Vasilev, Stefan
Contributors: Agricola, Ilka (Prof. Dr. habil.) (Thesis advisor)
Format: Doctoral Thesis
Language:English
Published: Philipps-Universität Marburg 2019
Subjects:
Nabla-Killing and nabla-confor
Metric connections with totally skew torsion
Mathematik
Zusammenhang <Mathematik>
Laplace operators with torsion
Laplace-Operator
Generalized Weitzenböck formula
Torsion <Mathematik>
Mathematics
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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.
Physical Description:77 Pages
DOI:10.17192/z2020.0088

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