On Lorentzian $\beta$-{K}enmotsu manifolds admitting Schouten-van Kampen connection

Abstract

The present article aims to study the Lorentzian $\beta$-{K}enmotsu manifolds ($\mathcal M_\beta$) admitting the Schouten-van Kampen connection (in brief, SVKC). We study $\mathcal M_\beta$ satisfying $\zeta$-concircularly flat and $\varphi$-concircularly flat conditions admitting SVKC. Also, we study $\mathcal M_\beta$ admitting the SVKC satisfying $\widetilde{C} \cdot \widetilde{S}=0$. We also deal the locally $\varphi$-Ricci symmetric $\mathcal M_\beta$ with respect to the SVKC. Further, we discussed almost Ricci solitons on $\mathcal M_\beta$ admitting SVKC. Finally, we have given an example of $\mathcal M_\beta$ admitting a SVKC which verifies some of our results.

Keywords

• Lorentzian $\beta$-{K}enmotsu manifolds
• concircular curvature tensor
• Schouten-van Kampen connection
• Ricci solitons.

Supporting Institution

Not Applicable

Project Number

Not Applicable

Ethical Statement

The authors declare that this manuscript is original, has not been published or submitted elsewhere, and contains no plagiarism. All authors have contributed to the work, approved the final version, and have no conflicts of interest. The paper complies with the ethical standards of the Ikonion Journal of Mathematics.

Thanks

The authors would like to thank the referee for some useful comments and their helpful suggestions that have improved the quality of this paper.

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