Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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STUDY OF 𝜼-RICCI-BOURGUIGNON SOLITONS ON 𝝃-CONFORMALLY FLAT LORENTZIAN PARA-KENMOTSU MANIFOLDS

  • Received : 2024.11.23
  • Accepted : 2025.06.12
  • Published : 2025.10.31
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Abstract

The aim of this study is to characterize the 𝜼-Ricci-Bourguignon soliton (briefly, 𝜼-𝓡𝓑𝓢) in the context of 𝝃-conformally flat Lorentzian para-Kenmotsu manifold. Further, we establish that the scalar curvature 𝜿 of a p-dimensional Lorentzian para-Kenmotsu (briefly, (𝓛𝓟𝓚)p) manifold admitting an 𝜼-𝓡𝓑𝓢 satisfies the Poisson's equation. Next, the condition for which the scalar curvature of (𝓛𝓟𝓚)p manifold admitting an 𝜼-𝓡𝓑𝓢 establishes Laplace equation. The presence of gradient 𝜼-𝓡𝓑𝓢 on (𝓛𝓟𝓚)p manifold has been established. At the end, an illustration of an (𝓛𝓟𝓚)4 manifold is constructed to confirm the results of this manuscript.

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References

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