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Smarandache Curves of Involute-Evolute Curve According to Frenet Frame

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

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.
Year 2023, Volume: 4 Issue: 1, 31 - 45, 31.01.2023
https://doi.org/10.54974/fcmathsci.1152564

Abstract

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.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Selin Sivas 0000-0001-9526-2414

Süleyman Şenyurt 0000-0003-1097-5541

Abdussamet Çalışkan 0000-0002-1512-2452

Publication Date January 31, 2023
Published in Issue Year 2023 Volume: 4 Issue: 1

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19113 FCMS is licensed under the Creative Commons Attribution 4.0 International Public License.