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Keywords = Bach tensor

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11 pages, 288 KiB  
Article
Characterization of Bach and Cotton Tensors on a Class of Lorentzian Manifolds
by Yanlin Li, M. S. Siddesha, H. Aruna Kumara and M. M. Praveena
Mathematics 2024, 12(19), 3130; https://doi.org/10.3390/math12193130 - 7 Oct 2024
Cited by 12 | Viewed by 1247
Abstract
In this work, we aim to investigate the characteristics of the Bach and Cotton tensors on Lorentzian manifolds, particularly those admitting a semi-symmetric metric ω-connection. First, we prove that a Lorentzian manifold admitting a semi-symmetric metric ω-connection with a parallel Cotton [...] Read more.
In this work, we aim to investigate the characteristics of the Bach and Cotton tensors on Lorentzian manifolds, particularly those admitting a semi-symmetric metric ω-connection. First, we prove that a Lorentzian manifold admitting a semi-symmetric metric ω-connection with a parallel Cotton tensor is quasi-Einstein and Bach flat. Next, we show that any quasi-Einstein Lorentzian manifold admitting a semi-symmetric metric ω-connection is Bach flat. Full article
(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)
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