Skip to main content
SpringerLink
Log in

Quaternionic Salkowski Curves and Quaternionic Similar Curves

  • Research Article
  • Published:
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

In this paper, we give the definitions and characterizations of quaternionic Salkowski, quaternionic anti-Salkowski and quaternionic similar curves in the Euclidean spaces E3 and E4. We obtain relationships between these curves and some special quaternionic curves such as quaternionic slant helices and quaternionic B2-slant helices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Struik DJ (1988) Lectures on classical differential geometry, vol 89b. Dover, New York, p 53002

    Google Scholar 

  2. Izumiya S, Takeuchi N (2004) New special curves and developable surfaces. Turk J Math 28:153–163

    MathSciNet  MATH  Google Scholar 

  3. Önder M, Kazaz M, Kocayiğit H, Kılıç O (2008) B2-slant helix in Euclidean 4-space E4. Int J Cont Math Sci 3(29):1433–1440

    MATH  Google Scholar 

  4. Salkowski E (1909) Zur Transformation von Raumkurven. Math Ann 66(4):517–557

    Article  MathSciNet  Google Scholar 

  5. Monterde J (2009) Salkowski curves revisited: a family of curves with constant curvature and non-constant torsion. Comput Aided Geom Design 26:271–278

    Article  MathSciNet  Google Scholar 

  6. El-Sabbagh MF, Ali AT (2013) Similar curves with variable transformations. Konuralp J Math 1(2):80–90

    MATH  Google Scholar 

  7. Önder M (2013) Null similar curves with variable transformations in the Minkowski 3-space E31 . Int J Appl Math 26(6):685–693

    MathSciNet  MATH  Google Scholar 

  8. Şahiner B, Önder M (2016) Slant helices, Darboux helices and similar curves in dual space D3. Math Morav 20(1):89–103

    Article  MathSciNet  Google Scholar 

  9. Bharathi K, Nagaraj M (1987) Quaternion valued function of a real variable Serret–Frenet formulae. Indian J Pure Appl Math 18(6):507–511

    MathSciNet  MATH  Google Scholar 

  10. Hacisalihoglu HH (1983) Hareket Geometrisi ve Kuaterniyonlar Teorisi. Gazi Üniversitesi Fen-Edebiyat Fakültesi Yayınları Mat No 2

  11. Ward JP (1997) Quaternions and Cayley numbers. Kluwer Academic Publishers, Boston

    Book  Google Scholar 

  12. Gök İ, Okuyucu OZ, Kahraman F, Hacisalihoğlu HH (2011) On the quaternionic B2-slant helix in the Euclidean space E4. Adv Appl Clifford Algebras 21:707–719

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Delibekirli Village, Tepe Street, No: 63, Kırıkhan, 31440, Turkey

    Mehmet Önder

Authors
  1. Mehmet Önder
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mehmet Önder.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Önder, M. Quaternionic Salkowski Curves and Quaternionic Similar Curves. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 90, 447–456 (2020). https://doi.org/10.1007/s40010-019-00601-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40010-019-00601-y

Keywords

Mathematics Subject Classification

Search

Navigation