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

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Abstract

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 \({{\mathbb{R}}^4_2}\).

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Authors and Affiliations

  1. Departamento de Matemática, ICMC, USP C.P. 668, São Carlos, SP, 13560-970, Brazil

    I. I. Onnis & A. Passos Passamani

Authors
  1. I. I. Onnis
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  2. A. Passos Passamani
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Correspondence to I. I. Onnis.

Additional information

A. Passos Passamani was supported by Capes–Brasil.

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Onnis, I.I., Passamani, A.P. On the Biharmonic Curves in the Special Linear Group \({{\mathbf{SL}}{\bf (2},{\mathbb{R}}{\bf )}}\) . Mediterr. J. Math. 13, 443–457 (2016). https://doi.org/10.1007/s00009-014-0474-2

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  • DOI: https://doi.org/10.1007/s00009-014-0474-2

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