Finally, we give two illustrative examples related to our results.
📌 3 Key Takeaways
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Objective & Hypothesis:Let the spacelike curve * be the involute of the 𝛼 timelike curve.
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Key Findings & Data:In this study, when the Frenet vectors of the involute curve 𝛼 ∗ are taken as the position vectors, the curvature and the torsion of non-null * * T B and * * N B - Smarandache curve are calculated depending upon the timelike evolute curve 𝛼.
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Conclusion & Impact:Finally, we give two illustrative examples related to our results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
Let the spacelike curve * be the involute of the 𝛼 timelike curve. In this study, when the Frenet vectors of the involute curve 𝛼 ∗ are taken as the position vectors, the curvature and the torsion of non-null * * T B and * * N B - Smarandache curve are calculated depending upon the timelike evolute curve 𝛼. Finally, we give two illustrative examples related to our results.
Özet
spacelike eğrisi, timelike eğrisinin bir involütü olsun. Bu çalışmada,*eğrisinin Frenet vektörleri konumvektörleri olarak alındığında null olmayan* * T Bve* * N B -Smarandache eğrilerinin eğrilik ve torsiyonlarıtimelike evolüt eğrisine bağlı olarak hesaplanmıştır. Son olarak, elde edilen sonuçlar ile ilgili örnekler verilmiştir.
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Cite This Article
KALKAN, Ö. B., ZEYBEK, D. (2022). T*B* and N*B*-Smarandache Curves of Involute-Evolute Curves in Minkowski 3-space. Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, Cilt: 8 - Sayı: 2, 472–483. https://ajindex.com/articles/466989
Bilici M., Çalışkan M. 2009. On the Involutes of Spacelike Curve with a Timelike Binormal in Minkowski 3-Space. International Mathematical Forum, 4 (31): 1497-1509
Bilici M., Çalışkan M. 2011. Some New Notes on the Involutes of the Timelike Curves in Minkowski 3-Space. International Journal of Contemporary Mathematical Sciences, 6 (41): 2019- 2030
Bükçü B., Karacan M.K. 2007. On the Involute and Evolute Curves of Spacelike Curves with a Spacelike Binormal in Minkowski 3-Space. International Journal of Mathematical. Sciences, 2 (5): 221-232
Bükçü B., Karacan M.K. 2007. On the Involute and Evolute Curves of the Timelike Curve in Minkowski 3-Space, Demostratio Mathematica, 40 (3): 721-732
Duggal K.L, Bejancu A. 1996. Lightlike Submanifolds of Semi Riemannian Manifolds and Applications. Kluwer Academic Publishers, Dordrecht
Gürses N., Bektaş Ö., Yüce S. 2016. Special Smarandache Curves in 3 R1. Communications Faculty of Sciences. University of Ankara Series. A1 Mathematics and Statics, 65 (2): 143-160
Kalkan Ö., Öztürk H., Zeybek D. 2018. On * * T N Smarandache Curves of Involute-Evolute Curve According to Frenet Frame in Minkowski 3-Space. 16 th. International Geometry Symposium, July 4-7, Manisa Celal Bayar University, Manisa
Lopez, R., 2014. Differential geometry of curves and surfaces in Lorentz-Minkowski space. International Electronic Journal of Geometry, 7 (1): 44-107
O’Neill B. 1983. Semi-Riemannian Geometry with Applications to Relativity. Academic Press, London
Şenyurt S., Sivas S. 2013. Smarandache Eğrilerine Ait Bir Uygulama. Ordu Universitesi. Journal of Science and Technology, 3 (1): 46-60
Şenyurt S., Çalışkan A. 2015. * * N C -Smarandache Curves of Mannheim Curve Couple According to Frenet Frame. International Journal of Mathematical, Combinatorics, 1: 1–13
Şenyurt S., Çalışkan A., Çelik Ü. 2016. * * N C -Smarandache Curve of Bertrand Curves Pair According to Frenet Frame, International Journal of Mathematical. Combinatorics, Vol.1: 1-7
Şenyurt S., Altun Y., Cevahir C. 2019. Smarandache Curves According to Sabban Frame Belonging to Mannheim Curves Pair. Communications Faculty of Sciences. University of Ankara Series. A1 Mathematics and Statics, 68 (1): 500-513
Şenyurt S., Altun Y., Cevahir C. 2020. Smarandache Curves for Spherical Indicatrix of the Bertrand Curves Pair. Boletim da Sociedade Paranaense de Mathematica, 38 (2): 27-39