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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We have also shown that if a $3$-dimensional trans-Sasakian manifold admits conformal gradient shrinking Ricci soliton, then the manifold is an Einstein manifold.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper we have shown that if a $3$-dimensional trans-Sasakian manifold M admits conformal Ricci soliton $(g,V,\lambda )$ and if the vector field $V$ is point wise collinear with the unit vector field $\xi$, then $V$ is a constant multiple of $\xi$.
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Key Findings & Data:Similarly we have proved that under the same condition an almost conformal Ricci soliton becomes conformal Ricci soliton.
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Conclusion & Impact:We have also shown that if a $3$-dimensional trans-Sasakian manifold admits conformal gradient shrinking Ricci soliton, then the manifold is an Einstein manifold.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:conformal Ricci soliton · almost conformal Ricci soliton · conformal gradient shrinking Ricci soliton
Abstract
In this paper we have shown that if a $3$-dimensional trans-Sasakian manifold M admits conformal Ricci soliton $(g,V,\lambda )$ and if the vector field $V$ is point wise collinear with the unit vector field $\xi$, then $V$ is a constant multiple of $\xi$. Similarly we have proved that under the same condition an almost conformal Ricci soliton becomes conformal Ricci soliton. We have also shown that if a $3$-dimensional trans-Sasakian manifold admits conformal gradient shrinking Ricci soliton, then the manifold is an Einstein manifold.
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Cite This Article
BHATTACHARYYA, A., DUTTA, T., BASU, N. (2022). Almost conformal Ricci solituons on $3$-dimensional trans-Sasakian manifold. Hacettepe Journal of Mathematics and Statistics, Cilt: 45 - Sayı: 5, 1379–1392. https://ajindex.com/articles/530231