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Journals / International Electronic Journal of Geometry / 2026 / Volume: 17 Issue: 1

$K$-Ricci-Bourguignon Almost Solitons

U.c. De(University of Calcutta)0000-0002-8990-4609
Krishnendu De(Kabi Sukanta Mahavidyalaya, The University of Burdwan)0000-0001-6520-4520
Pages
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Publication Date
2024-04-23
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⚡ TL;DR(Too Long; Didn't Read)

Moreover, we illustrate that the spacetime represents a perfect fluid spacetime and the divergence of the Weyl tensor vanishes if a generalized Robertson-Walker spacetime admits a $K$-Ricci-Bourguignon almost soliton.

📌 3 Key Takeaways

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Objective & Hypothesis:We in this current article introduce and characterize a $K$-Ricci-Bourguignon almost solitons in perfect fluid spacetimes and generalized Robertson-Walker spacetimes.
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Key Findings & Data:First, we demonstrate that if a perfect fluid spacetime admits a $K$-Ricci-Bourguignon almost soliton, then the integral curves produced by the velocity vector field are geodesics and the acceleration vector vanishes.
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Conclusion & Impact:Moreover, we illustrate that the spacetime represents a perfect fluid spacetime and the divergence of the Weyl tensor vanishes if a generalized Robertson-Walker spacetime admits a $K$-Ricci-Bourguignon almost soliton.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Perfect fluid spacetimes · GRW spacetimes · $K$ Ricci-Bourguignon solitons

Abstract

We in this current article introduce and characterize a $K$-Ricci-Bourguignon almost solitons in perfect fluid spacetimes and generalized Robertson-Walker spacetimes. First, we demonstrate that if a perfect fluid spacetime admits a $K$-Ricci-Bourguignon almost soliton, then the integral curves produced by the velocity vector field are geodesics and the acceleration vector vanishes. Then we establish that if perfect fluid spacetimes permit a gradient $K$-Ricci-Bourguignon soliton with Killing velocity vector field, then either state equation of the perfect fluid spacetime is presented by $p=\frac{3-n}{n-1}\sigma$ , or the gradient $K$-Ricci-Bourguignon soliton is shrinking or expanding under some condition. Moreover, we illustrate that the spacetime represents a perfect fluid spacetime and the divergence of the Weyl tensor vanishes if a generalized Robertson-Walker spacetime admits a $K$-Ricci-Bourguignon almost soliton.

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Cite This Article

De, U., De, K. (2024). $K$-Ricci-Bourguignon Almost Solitons. International Electronic Journal of Geometry, Volume: 17 Issue: 1. https://doi.org/10.36890/iejg.1434598

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