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Characterizations of Ricci–Bourguignon Almost Solitons on Pseudo-Riemannian Manifolds

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Abstract

In this paper, we thoroughly study the Ricci–Bourguignon almost soliton and gradient Ricci–Bourguignon almost soliton on paracontact metric manifolds. First we find some sufficient conditions under which a paracontact metric manifolds admitting a Ricci–Bourguignon almost soliton is Einstein (trivial). Next we prove that if a para-Sasakian manifold admits a gradient Ricci–Bourguignon almost soliton, it is Einstein (trivial) with constant scalar curvature \(-2n(2n+1)\). It is locally isometric to a flat manifold product and a manifold of constant curvature \(-4\) if it is for \((k, \mu )\)-paracontact manifold admits a gradient Ricci–Bourguignon almost soliton.

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Acknowledgements

The authors thank the referees for their valuable and constructive comments for modifying the presentation of this work. Also, the authors would like to express their gratitude to Prof. Ramesh Sharma and Prof. Amalendu Ghosh for their improving comments the manuscript. The authors would like to express their gratitude to the Deanship of Scientific Research at King Khalid University, Saudi Arabia for providing a funding research group under the research grant R. G. P. 1/50/42. The authors also express their gratitude to Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2022R27), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology - Hyderabad, Sangareddy, 502285, Hyderabad, India

    Dhriti Sundar Patra

  2. Department of Mathematics, King Khalid University, Abha, 9004, Saudi Arabia

    Akram Ali

  3. Mathematical Science Department Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh, 11546, Saudi Arabia

    Fatemah Mofarreh

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  1. Dhriti Sundar Patra
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  2. Akram Ali
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Correspondence to Fatemah Mofarreh.

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Patra, D.S., Ali, A. & Mofarreh, F. Characterizations of Ricci–Bourguignon Almost Solitons on Pseudo-Riemannian Manifolds. Mediterr. J. Math. 19, 176 (2022). https://doi.org/10.1007/s00009-022-02085-4

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  • DOI: https://doi.org/10.1007/s00009-022-02085-4

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