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A Note on Recurrent Bivectors in 4-Dimensional Lorentz Manifolds
Marmara University, Faculty of Arts and Sciences, Department of Mathematics, Istanbul, Turkey
Abstract: We study recurrence properties of the second order skew-symmetric tensor fields, which are referred to as bivectors, on a 4-dimensional manifold admitting a Lorentz metric. Considering the known classification scheme for these tensor fields, recurrent bivectors which can be scaled to be parallel are first determined and these results are associated with the holonomy theory. This examination then identifies proper recurrence of such bivectors on the manifold. The link between these bivectors and the holonomy group is investigated and some theorems are proved.
Keywords: bivector, recurrent tensor, Lorentz signature, holonomy
Classification (MSC2000): 53C29; 53C50
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Electronic fulltext finalized on: 26 Apr 2018.
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