Certain results on generalized (k,μ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{(k,\,\mu )}}$$\end{document}-contact metric manifolds

被引：4
作者：
U. C. De
Krishanu Mandal
机构：
[1] University of Calcutta,Department of Pure Mathematics
来源：
Journal of Geometry | 2017年 / 108卷 / 2期
关键词：
Generalized (; )-contact manifold; second order parallel tensor; Ricci soliton; Sasakian manifold; 53C15; 53C25;
D O I：
10.1007/s00022-016-0362-y
中图分类号：
学科分类号：
摘要：
The object of the present paper is to study second order symmetric parallel tensors in generalized (k,μ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k,\,\mu )$$\end{document}-contact metric manifolds and its applications to Ricci solitons. Next, we prove that a generalized (k,μ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k,\,\mu )$$\end{document}-contact metric manifold M admits a Ricci soliton whose potential vector field is the Reeb vector field ξ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\xi $$\end{document} if and only if M is a Sasaki–Einstein manifold. Finally, we give some examples of generalized (k,μ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(k,\,\mu )$$\end{document}-contact metric manifold.
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收藏
页码：611 / 621
页数：10
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