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

Yanlin Li (), M. S. Siddesha, H. Aruna Kumara and M. M. Praveena
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Yanlin Li: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
M. S. Siddesha: Department of Data Analytics and Mathematical Science, Jain (Deemed to be University), Global Campus, Bangalore 562112, India
H. Aruna Kumara: Department of Mathematics, BMS Institute of Technology and Management, Yelahanka, Bangalore 560064, India
M. M. Praveena: Department of Mathematics, M. S. Ramaiah Institute of Technology, Bangalore 560054, India

Mathematics, 2024, vol. 12, issue 19, 1-11

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 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.

Keywords: Bach tensor; Cotton tensor; Lorentzian manifolds; semi-symmetric metric connection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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