On the Biharmonic Curves in the Special Linear Group \({{\mathbf{SL}}{\bf (2},{\mathbb{R}}{\bf )}}\)

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• 作者：I. I. Onnis ; A. Passos Passamani
• 关键词：53C30 ; 58E20 ; Special linear group ; biharmonic curves ; helix curves ; homogeneous spaces
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：13
• 期：1
• 页码：443-457
• 全文大小：551 KB
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• 作者单位：I. I. Onnis (1)
  A. Passos Passamani (1)
  
  1. Departamento de Matemática, ICMC, USP C.P. 668, São Carlos, SP, 13560-970, Brazil
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454

文摘

We characterize the biharmonic curves in the special linear group \({\mathrm{SL}(2,{\mathbb{R}})}\). In particular, we show that all proper biharmonic curves in \({\mathrm{SL}(2,{\mathbb{R}})}\) are helices and we give their explicit parametrizations as curves in the pseudo-Euclidean space \({{\mathbb{R}}^4_2}\). Mathematics Subject Classification 53C30 58E20