Moreover, we introduce the concept ofthe generalized Ricci soliton and we suggest the method of constructionof the Riemannian manifold $(M, g)$ with a Ricci soliton $g$.Finally, we also study the Lorentzian warped products with the Riccisoliton.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we study the Ricci soliton in the Riemannian products$M=R^n \times B$ and warped products $M=R \times _f B$ of theEuclidean space and Riemannian manifolds, and the gradient Riccisoliton in the warped products $M=S^1 \times _f B$ of 1-dimensionalcircle and Riemannian manifolds.
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Key Findings & Data:In this paper, we study the Ricci soliton in the Riemannian products$M=R^n \times B$ and warped products $M=R \times _f B$ of theEuclidean space and Riemannian manifolds, and the gradient Riccisoliton in the warped products $M=S^1 \times _f B$ of 1-dimensionalcircle and Riemannian manifolds.
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Conclusion & Impact:Moreover, we introduce the concept ofthe generalized Ricci soliton and we suggest the method of constructionof the Riemannian manifold $(M, g)$ with a Ricci soliton $g$.Finally, we also study the Lorentzian warped products with the Riccisoliton.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Ricci curvature · warped product space · Ricci soliton
Abstract
In this paper, we study the Ricci soliton in the Riemannian products$M=R^n \times B$ and warped products $M=R \times _f B$ of theEuclidean space and Riemannian manifolds, and the gradient Riccisoliton in the warped products $M=S^1 \times _f B$ of 1-dimensionalcircle and Riemannian manifolds. Moreover, we introduce the concept ofthe generalized Ricci soliton and we suggest the method of constructionof the Riemannian manifold $(M, g)$ with a Ricci soliton $g$.Finally, we also study the Lorentzian warped products with the Riccisoliton.
LEE, S. D., KIM, B. H., CHOI, J. H. (2022). Warped product spaces with Ricci conditions. Turkish Journal of Mathematics, Cilt: 41 - Sayı: 6, 1365–1375. https://ajindex.com/articles/607993