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<p>We generalize the criteria proposed by Z. Soyuçok in the 3-dimensional Euclidean space to the Lorentz 3-space for the timelike surfaces. With an aid of this criterion we investigate nonisothermic timelike Bonnet surfaces and their associate surfaces. Finally, we consider the classification of helicoids proposed by Beneki et al. We present nonisothermic timelike helicoids as examples illustrating our results. Thus, they satisfy the conditions as timelike Bonnet surfaces. In addition, we present the isothermic timelike minimal helicoids.</p>

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Timelike Bonnet Surfaces in the Lorentzian 3-Space

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Filiz Kanbay,
  • Burcu Yüksekdağ

摘要

We generalize the criteria proposed by Z. Soyuçok in the 3-dimensional Euclidean space to the Lorentz 3-space for the timelike surfaces. With an aid of this criterion we investigate nonisothermic timelike Bonnet surfaces and their associate surfaces. Finally, we consider the classification of helicoids proposed by Beneki et al. We present nonisothermic timelike helicoids as examples illustrating our results. Thus, they satisfy the conditions as timelike Bonnet surfaces. In addition, we present the isothermic timelike minimal helicoids.