Trans-Sasakian Manifolds Homothetic to Sasakian Manifolds

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• 作者：Sharief Deshmukh
• 关键词：Almost contact metric manifold ; Sasakian manifold ; trans ; Sasakian manifold ; Poisson equation
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：13
• 期：5
• 页码：2951-2958
• 全文大小：470 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454
• 卷排序：13

文摘

In this paper, it is shown that for a 3-dimensional compact simply connected trans-Sasakian manifold of type \({(\alpha,\beta)}\), the smooth functions \({\alpha,\beta}\) satisfy the Poisson equations \({\Delta \alpha = \beta}\), \({\Delta \alpha = \alpha ^{2}\beta}\) and \({\Delta \beta = \alpha ^{2}\beta}\), respectively, if and only if it is homothetic to a Sasakian manifold. We also find a necessary and sufficient condition for a connected 3-dimensional trans-Sasakian manifold of type \({(\alpha,\beta)}\) in terms of a differential equation satisfied by the smooth function \({\alpha}\) to be homothetic to a Sasakian manifold.