Smarandache Curves of Involute-Evolute Curve According to Frenet Frame

Year 2023, Volume: 4 Issue: 1, 31 - 45, 31.01.2023

Selin Sivas , Süleyman Şenyurt , Abdussamet Çalışkan

https://doi.org/10.54974/fcmathsci.1152564

Abstract

In this paper, the invariants of the Smarandache curves, which consist of Frenet vectors of the involute curve, are calculated in terms of the evolute curve.

Keywords

Curvature, Evolute curve, Frenet frame, Involute curve, Smarandache curves, Torsion.

References

• Al-Dayel I., Solouma E.M., Geometric properties in Minkowski space-time of spacelike Smarandache curves, International Journal of Applied and Computational Mathematics, 7(4), 1-16, 2021.
• Ali A.T., Special Smarandache curves in the euclidean space, International Journal of Mathematical Combinatorics, 2, 30-36, 2010.
• As E., Sarıoğlugil A., On the Bishop curvatures of involute-evolute curve couple in E3 , International Journal of Physical Sciences, 9(7), 140-145, 2014.
• Bektaş Ö., Yüce S., Special Smarandache curves according to Dardoux frame in Euclidean 3-space, Romanian Journal of Mathematics and Computer science, 3, 48-59, 2013.
• Bilici M., Çalışkan M., Some new notes on the involutes of the timelike curves in Minkowski 3-space, International Journal of Contemporary Mathematical Sciences, 6(41), 2019-2030, 2011.
• Ergüt M., Yılmaz S., Ünlütürk Y., Isotropic Smarandache curves in the complex 4-space, Honam Mathematical Journal, 40(1), 47-59, 2018.
• Hacısalihoğlu H.H., Differential Geometry (in Turkish), İnönü University, Malatya, 1983.
• Millman R.S., Parker G.D., Elements of Differential Geometry, Prentice-Hall Inc., Englewood Cliffs, 1977.
• Nurkan S.K., Güven I., A new approach for Smarandache curves, Turkish Journal of Mathematics and Computer Science, 14(1), 155-165, 2022.
• Sabuncuoğlu A., Differential Geometry (in Turkish), Nobel Publications, Ankara, 2006.
• Samancı H.K., Cengiz V., Dual Smarandache curves and ruled surfaces obtained from the alternative frame, Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 12(2), 512-526, 2022.
• Şenyurt S., Çalışkan A., Smarandache curves in terms of Sabban frame of fixed pole curve, Boletimda Sociedade Paranaense de Matematica, 34(2), 53-62, 2016.
• Şenyurt S., Sivas S., Çalışkan A., N*C*-Smarandache curves of involute evolute curve couple according to Frenet frame algebras, Algebras Groups and Geometries, 33(2), 153-164, 2016.
• Şenyurt S., Çalışkan A., Çelik U., Smarandache curves of Bertrand curves pair according to Frenet frame, Boletim da Sociedade Paranaense de Matematica, 39(5), 163-173, 2021.
• Şenyurt S., Cevahir C., Altun Y., On the Smarandache curves of spatial quaternionic involute curve, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 90(5), 827-837, 2020.
• Taşköprü K., Tosun M., Smarandache curves according to Sabban frame on S2 , Boletim da Sociedade Paranaense de Matematica, 32(1), 51-59, 2014.
• Turgut M., Yılmaz S., Smarandache curves in Minkowski spacetime, International Journal of Mathematical Combinatorics, 3, 51-55, 2008.