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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
We then explicitly write this equation on the Poincar\'e disk $\mathbb{D}^2$ equipped with the hyperbolic metric in polar coordinates.
📌 3 Key Takeaways
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Objective & Hypothesis:We present a new concept of $(h,\eta)$-Ricci-Bourguignon Soliton on a Riemannian manifold $(M,g)$ defined by \begin{equation}\label{eq1} \mathrm{Ric}+\frac{h}{2}\,\mathcal{L}_X g=(\lambda+\rho\,\mathrm{Scal})\,g + \omega\,\eta\otimes\eta, \end{equation} where $\eta$ is a $1$-form, $h$ is a non-zero smooth function, and $\lambda$, $\rho$ and $\omega$ are real constants, denoted by \textbf{$(M,g,X,\lambda,\rho,\omega)$}.
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Key Findings & Data:We present a new concept of $(h,\eta)$-Ricci-Bourguignon Soliton on a Riemannian manifold $(M,g)$ defined by \begin{equation}\label{eq1} \mathrm{Ric}+\frac{h}{2}\,\mathcal{L}_X g=(\lambda+\rho\,\mathrm{Scal})\,g + \omega\,\eta\otimes\eta, \end{equation} where $\eta$ is a $1$-form, $h$ is a non-zero smooth function, and $\lambda$, $\rho$ and $\omega$ are real constants, denoted by \textbf{$(M,g,X,\lambda,\rho,\omega)$}.
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Conclusion & Impact:We then explicitly write this equation on the Poincar\'e disk $\mathbb{D}^2$ equipped with the hyperbolic metric in polar coordinates.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:η)-Ricci-Bourguignon Soliton · Hyperbolic Disk · Beltrami-Laplacian.
Abstract
We present a new concept of $(h,\eta)$-Ricci-Bourguignon Soliton on a Riemannian manifold $(M,g)$ defined by \begin{equation}\label{eq1} \mathrm{Ric}+\frac{h}{2}\,\mathcal{L}_X g=(\lambda+\rho\,\mathrm{Scal})\,g + \omega\,\eta\otimes\eta, \end{equation} where $\eta$ is a $1$-form, $h$ is a non-zero smooth function, and $\lambda$, $\rho$ and $\omega$ are real constants, denoted by \textbf{$(M,g,X,\lambda,\rho,\omega)$}. We then explicitly write this equation on the Poincar\'e disk $\mathbb{D}^2$ equipped with the hyperbolic metric in polar coordinates.
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Cite This Article
Diop, M. N., Bousso, A., Ndiaye, A., Mandal, A. (2026). $(h,\eta)$-Ricci-Bourguignon Soliton on the Poincare Disk $\mathbb{D}^2$. Konuralp Journal of Mathematics, Volume: 14 Issue: 1. https://ajindex.com/articles/1521445