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Volume 12
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10.3390/math12193130
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Article

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

by
Yanlin Li
1,*,†,
M. S. Siddesha
2,†,
H. Aruna Kumara
3,† and
M. M. Praveena
4,†
1
School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
2
Department of Data Analytics and Mathematical Science, Jain (Deemed to be University), Global Campus, Bangalore 562112, India
3
Department of Mathematics, BMS Institute of Technology and Management, Yelahanka, Bangalore 560064, India
4
Department of Mathematics, M. S. Ramaiah Institute of Technology, Bangalore 560054, India
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2024, 12(19), 3130; https://doi.org/10.3390/math12193130
Submission received: 1 September 2024 / Revised: 30 September 2024 / Accepted: 5 October 2024 / Published: 7 October 2024
(This article belongs to the Special Issue Recent Studies in Differential Geometry and Its Applications)
Versions Notes

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 Bach tensor; Cotton tensor; Lorentzian manifolds; semi-symmetric metric connection

Share and Cite

MDPI and ACS Style

Li, Y.; Siddesha, M.S.; Kumara, H.A.; Praveena, M.M. Characterization of Bach and Cotton Tensors on a Class of Lorentzian Manifolds. Mathematics 2024, 12, 3130. https://doi.org/10.3390/math12193130

AMA Style

Li Y, Siddesha MS, Kumara HA, Praveena MM. Characterization of Bach and Cotton Tensors on a Class of Lorentzian Manifolds. Mathematics. 2024; 12(19):3130. https://doi.org/10.3390/math12193130

Chicago/Turabian Style

Li, Yanlin, M. S. Siddesha, H. Aruna Kumara, and M. M. Praveena. 2024. "Characterization of Bach and Cotton Tensors on a Class of Lorentzian Manifolds" Mathematics 12, no. 19: 3130. https://doi.org/10.3390/math12193130

APA Style

Li, Y., Siddesha, M. S., Kumara, H. A., & Praveena, M. M. (2024). Characterization of Bach and Cotton Tensors on a Class of Lorentzian Manifolds. Mathematics, 12(19), 3130. https://doi.org/10.3390/math12193130

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