Ricci–Bourguignon Soliton on Three-Dimensional Contact Metric Manifolds

被引:0
作者
Mohan Khatri
Jay Prakash Singh
机构
[1] Pachhunga University College,Department of Mathematics
[2] Central University of South Bihar,Department of Mathematics
来源
Mediterranean Journal of Mathematics | 2024年 / 21卷
关键词
Ricci–Bourguignon soliton; sasakian; lie group; contact metric manifolds; isometry; Primary 53C15; Secondary 53C20; 53C25;
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摘要
This paper aims to classify a certain type of three-dimensional complete non-Sasakian contact manifold with specific properties, namely Qξ=σξ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q\xi =\sigma \xi $$\end{document} and admitting Ricci–Bourguignon solitons. In the case of constant σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma $$\end{document}, the paper proves that if the potential vector field of the Ricci–Bourguignon soliton is orthogonal to the Reeb vector field, then the manifold is either Einstein or locally isometric to E(1, 1). Under a similar hypothesis, the paper shows that a (κ,μ,ϑ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(\kappa ,\mu ,\vartheta )$$\end{document}-contact metric manifold is locally isometric to E(1, 1). Finally, the paper considers the scenario where the potential vector is pointwise collinear with the Reeb vector field and presents some results.
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