Sasakian metrics as generalized η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-Ricci soliton

被引：0
作者：
Amalendu Ghosh
机构：
[1] Chandernagore College,Department of Mathematics
来源：
Periodica Mathematica Hungarica | 2023年 / 86卷 / 1期
关键词：
Generalized ; -Ricci soliton; -Ricci soliton; Ricci soliton; Contact metric manifold; -Einstein; Contact vector field; Sasakian manifold; 53C25; 53C44; 53D10;
D O I：
10.1007/s10998-022-00462-w
中图分类号：
学科分类号：
摘要：
In this paper, we consider Sasakian metric as a proper η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-Ricci almost soliton and prove that it is isometric to a unit sphere S2n+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S^{2n+1}$$\end{document}, provided the dimension of the manifold is greater than 3. Next, we prove that if a Sasakian manifold admitting a generalized η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-Ricci soliton whose potential vector field is a contact vector field is η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-Einstein and the potential vector field is Killing. Finally, we prove that a complete Sasakian manifold of dimension greater than 3 is isometric to a unit sphere if it admits a non-trivial gradient generalized η\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\eta $$\end{document}-Ricci soliton.
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页码：139 / 151
页数：12
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