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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 51 Issue: 5

Characterization of proper curves and proper helix lying on $S_{1}^2(r)$

Buddhadev Pal(Banaras Hindu University)0000-0002-1407-1016
Santosh Kumar(Banaras Hindu University)0000-0003-0571-9631
Sayfa
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Yayın Tarihi
2022-10-01
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, we find the condition for curve $\gamma(s)$ to lie in a plane.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we analyse the proper curve $\gamma(s)$ lying on the pseudo-sphere.
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Temel Bulgular & Veri:We develop an orthogonal frame $\lbrace V_{1}, V_{2}, V_{3} \rbrace$ along the proper curve, lying on pseudosphere.
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Sonuç & Katkı:Finally, we find the condition for curve $\gamma(s)$ to lie in a plane.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Minkowski space · pseudo sphere · proper helix of order 2

Abstract

In this paper, we analyse the proper curve $\gamma(s)$ lying on the pseudo-sphere. We develop an orthogonal frame $\lbrace V_{1}, V_{2}, V_{3} \rbrace$ along the proper curve, lying on pseudosphere. Next, we find the condition for $\gamma(s)$ to become $V_{k} -$ slant helix in Minkowski space. Moreover, we find another curve $\beta(\bar{s})$ lying on pseudosphere or hyperbolic plane heaving $V_{2} = \bar{V_{2}}$ for which $\lbrace \bar{V_{1}},\bar{V_{2}},\bar{V_{3}} \rbrace$, an orthogonal frame along $\beta(\bar{s})$. Finally, we find the condition for curve $\gamma(s)$ to lie in a plane.

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Bu Makaleye Atıf Yap

Pal, B., Kumar, S. (2022). Characterization of proper curves and proper helix lying on $S_{1}^2(r)$. Hacettepe Journal of Mathematics and Statistics, Volume: 51 Issue: 5. https://doi.org/10.15672/hujms.960966

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