A NEW GLANCE TO THE ASPECTS OF Q-HELICES

Yasin Unluturk, Cumali Ekici, Dogan Unal

DOI Number
https://doi.org/10.22190/FUMI221122004U
First page
051
Last page
065

Abstract


In this examination, we take q-helices into consideration. By q-helices, we mean curves due to the quasi-frame (abbv. q-frame) whose vector fields make constant angles with a non-zero fixed axis. One by one, all types of these q-helices we study in the work are therefore classified in three dimensional Euclidean space. Additionally, we study Darboux q-helices by using Darboux vector obtained with respect to q-frames fields of a curve. For a curve enclosed with q-frame as a general case, we reach some results for Darboux q-helices.


Keywords

q-frame, q-helices, the relations between q-helices, Darboux q-helices

Full Text:

PDF

References


A. Al˙I, R. Lopez and M. Turgut: k−type partially null and pseudo null slant helices in Minkowski 4-space. Math. Commun. 17 (2012), 93–103.

R. L. Bishop: There is more than one way to frame a curve. Am. Math. Mon. 82 (1975), 246–251.

S. Coquillart: Computing offsets of B-spline curves. Computer-Aided Design 19 (1987), 305–309.

M. Dede, C. Ek˙ıc˙ı and A. G¨org¨ul¨u: Directional q-frame along a space curve. IJARCSSE 5 (2015), 775–780.

M. Dede, C. Ek˙ıc˙ı and ˙I. G¨uven: Directional Bertrand Curves. GU. J. Sci. 31 (2018), 202–211.

M. Dede, M. C¸ . Aslan, and C. Ek˙ıc˙ı: On a variational problem due to the BDarboux frame in Euclidean 3-spaces. Math. Meth. Appl. Sci. 44 (2021), 12630–12639.

P. M. Do Carmo: Differential Geometry of Curves and Surfaces. Prentice-Hall Inc. Englewood Cliffs, New Jersey, 1976.

M. Erg¨ut, H. B. ¨Oztek˙ın and S. Aykurt: Non-null k−slant helices and their spherical indicatrices in Minkowski 3-space. J. Adv. Res. Dyn. Control Syst. 2 (2021), 1–12.

S. Izum˙ıya and N. Takeuch˙ı: New special curves and developable surfaces. Turk. J. Math. 28 (2004), 531–537.

L. Kula and Y. Yaylı: On slant helix and its spherical indicatrix. Appl. Math. Comput. 169 (2005), 600–607.

L. Kula, N. Ekmekc¸˙ı, Y. Yaylı and K. ˙Ilarslan: Characterizations of slant helices in Euclidean 3-space. Turk. J. Math. 34 (2010), 261–273.

R. S. Millman and G. D. Parker: Elements of Differential Geometry. Prentice-Hall Inc. Englewood Cliffs, New Jersey, 1977.

E. Nesovic, U. ¨Ozt¨urk and E. B. Koc¸ ¨Ozt¨urk: On k−type pseudo null Darboux helices in Minkowski 3-space. Math. Anal. Appl. 439 (2016), 690–700.

E. Nesovic, E. B. Koc¸ ¨Ozt¨urk and U. ¨Ozt¨urk: On k−type null Cartan slant helices in Minkowski 3-space. Math. Meth. Appl. Sci. 41 (2018), 7583–7598.

E. Nesovic, U. ¨Ozt¨urk and E. B. Koc¸ ¨Ozt¨urk: On T-Slant, N-Slant and B-Slant helices in Galilean space G3. J. Dyn. Syst. Geom. Theor. 16 (2018), 187–199.

U. ¨Ozt¨urk and E. Nesovic: On pseudo null and null Cartan Darboux helices in Minkowski 3-space. Kuwait J. Sci. 43 (2016), 64-82.

U. ¨Ozt¨urk and Z. B. Alkan: Darboux helices in three dimensional Lie groups. AIMS Mathematics 5 (2020), 3169–3181.

J. Quian and Y. Ho Kim: Null helix and k-type null slant helices in E4 1 . Rev. Un. Mat. Argentina 57 (2016), 71–83.

H. Shin, S. K. Yoo, S. K. Cho and W. H. Chung: Directional Offset of a Spatial Curve for Practical Engineering Design. ICCSA 3 (2003), 711–720.

D. J. Struik: Lectures on Classical Differential Geometry. Dover, New York, 1988.

M. Turgut and S. Yılmaz: Characterizations of some special helices in E4. Sci. Magna 4 (2008), 51–55.

G. U˘gur Kaymanlı, C. Ek˙ıc˙ı and M. Dede: Directional evolution of the ruled surfaces via the evolution of their directrix using q-frame along a timelike space curve. EJOSAT 20 (2020), 392–396.

Y. ¨Unl¨ut¨urk and T. K¨orpınar: On Darboux helices in Complex space C3. JOSA 4 (2019), 851–858.

S. Yılmaz, and M. Turgut: A new version of Bishop frame and an application to spherical images. J. Math. Anal. Appl. 371 (2010), 764–776.

E. Zıplar, A. S¸enol and Y. Yaylı: On Darboux helices in Euclidean 3-space. Glob. J. Sci. Front. Res. 12 (2012), 73–80.




DOI: https://doi.org/10.22190/FUMI221122004U

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)