Characterization of Bach and Cotton Tensors on a Class of Lorentzian Manifolds

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 i...

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Bibliographic Details
Published inMathematics (Basel) Vol. 12; no. 19; p. 3130
Main Authors Li, Yanlin, Siddesha, M. S., Kumara, H. Aruna, Praveena, M. M.
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.10.2024
Subjects
Bach tensor
Cotton tensor
Investigations
Lorentzian manifolds
Manifolds (mathematics)
semi-symmetric metric connection
Tensors
Theory of relativity
Topological manifolds
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12193130