IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v40y2009i5p2590-2596.html
   My bibliography  Save this article

Harmonic curvatures and generalized helices in En

Author

Listed:
  • Camcı, Çetin
  • İlarslan, Kazım
  • Kula, Levent
  • Hacısalihoğlu, H. Hilmi

Abstract

In n-dimensional Euclidean space En, harmonic curvatures of a non-degenerate curve defined by Özdamar and Hacisalihoğlu [Özdamar E, Hacısalihoglu HH. A characterization of Inclined curves in Euclidean n-space. Comm Fac Sci Univ Ankara, Ser A1 1975;24:15–23]. In this paper, we give some characterizations for a non-degenerate curve α to be a generalized helix by using its harmonic curvatures. Also we define the generalized Darboux vector D of a non-degenerate curve α in n-dimensional Euclidean space En and we show that the generalized Darboux vector D lies in the kernel of Frenet matrix M(s) if and only if the curve α is a generalized helix in the sense of Hayden.

Suggested Citation

  • Camcı, Çetin & İlarslan, Kazım & Kula, Levent & Hacısalihoğlu, H. Hilmi, 2009. "Harmonic curvatures and generalized helices in En," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2590-2596.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2590-2596
    DOI: 10.1016/j.chaos.2007.11.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907009393
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.11.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Falcón, Sergio & Plaza, Ángel, 2008. "On the 3-dimensional k-Fibonacci spirals," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 993-1003.
    2. El Naschie, M.S., 2005. "Experimental and theoretical arguments for the number and the mass of the Higgs particles," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1091-1098.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Külahcı, Mihriban & Bektaş, Mehmet & Ergüt, Mahmut, 2009. "On harmonic curvatures of a Frenet curve in Lorentzian space," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1668-1675.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Akbulak, Mehmet & Bozkurt, Durmuş, 2009. "On the order-m generalized Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1347-1355.
    2. Şenol, Ali & Yayli, Yusuf, 2009. "LC helices in space forms," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2115-2119.
    3. El Naschie, M.S., 2008. "Bounds on the number of possible Higgs particles using grand unification and exceptional Lie groups," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 633-637.
    4. Marek-Crnjac, L., 2006. "Different Higgs models and the number of Higgs particles," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 575-579.
    5. El Naschie, M.S., 2005. "Kähler-like manifolds, Weyl spinor particles and E-infinity high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 665-670.
    6. El Naschie, M.S., 2005. "Determining the mass of the Higgs and the electroweak bosons," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 899-905.
    7. Falcón, Sergio & Plaza, Ángel, 2007. "The k-Fibonacci sequence and the Pascal 2-triangle," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 38-49.
    8. Falcón, Sergio & Plaza, Ángel, 2008. "On the 3-dimensional k-Fibonacci spirals," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 993-1003.
    9. El Naschie, M.S., 2008. "Exact non-perturbative derivation of gravity’s G¯4 fine structure constant, the mass of the Higgs and elementary black holes," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 346-359.
    10. Tanaka, Yosuke, 2007. "The mass spectrum of heavier hadrons and E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 996-1007.
    11. ElOkaby, Ayman A., 2007. "A short review of the Higgs boson mass and E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 14-25.
    12. He, Ji-Huan, 2007. "E-Infinity theory and the Higgs field," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 782-786.
    13. Marek-Crnjac, L., 2007. "The maximum number of elementary particles in a super symmetric extension of the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1631-1636.
    14. Ekici, Erdal & Noiri, Takashi, 2009. "Decompositions of continuity, α-continuity and AB-continuity," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2055-2061.
    15. Naschie, M.S. El, 2005. "On the possibility of six gravity related particles in the standard model of high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1491-1496.
    16. Külahcı, Mihriban & Bektaş, Mehmet & Ergüt, Mahmut, 2009. "On harmonic curvatures of a Frenet curve in Lorentzian space," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1668-1675.
    17. Bijendra Singh & Kiran Sisodiya & Farooq Ahmad, 2014. "On the Products of -Fibonacci Numbers and -Lucas Numbers," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-4, June.
    18. El Naschie, M.S., 2005. "On a class of fuzzy Kähler-like manifolds," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 257-261.
    19. Falcón, Sergio & Plaza, Ángel, 2007. "On the Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1615-1624.
    20. Falcón, Sergio & Plaza, Ángel, 2008. "The k-Fibonacci hyperbolic functions," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 409-420.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2590-2596. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.