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arXiv · 1206.4072

Time-like constant slope surfaces and space-like Bertrand curves in Minkowski 3-space

Murat Babaarslan·Yusuf Yayli
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Abstract

Defining Lorentzian Sabban frame of the unit speed time-like curves on de Sitter 2-space $\mathbb{S}^{2}_{1}$ and introducing space-like height function on the unit speed time-like curves on $\mathbb{S}^{2}_{1}$, the invariants of the unit speed time-like curves on $\mathbb{S}^{2}_{1}$ and geometric properties of de Sitter evolutes of the unit speed time-like curves on $\mathbb{S}^{2}_{1}$ are studied. A relation between space-like Bertrand curves and helices is obtained. De Sitter Darboux images of space-like Bertrand curves are equal to de Sitter evolutes. The relations between time-like constant slope surfaces lying in the space-like cone and space-like Bertrand curves in Minkowski 3-space $\mathbb{R}^{3}_{1}$ are obtained.

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Murat Babaarslan, Yusuf Yayli. 2012-06-18. Time-like constant slope surfaces and space-like Bertrand curves in Minkowski 3-space. https://doi.org/10.1007/s40010-014-0160-6

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