호남수학학술지 (Honam Mathematical Journal)

  • 제45권1호
  • /
  • Pages.130-145
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  • 2023
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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INTEGRAL CURVES CONNECTED WITH A FRAMED CURVE IN 3-SPACE

  • Mustafa Duldul (Department of Mathematics, Yildiz Technical University) ;
  • Zeynep Bulbul (Department of Mathematics, Yildiz Technical University)
  • 투고 : 2022.09.06
  • 심사 : 2022.12.03
  • 발행 : 2023.03.25
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초록

In this paper, we define some integral curves connected with a framed curve in Euclidean 3-space. These curves include framed generalized principal-direction curve, framed generalized binormal-direction curve, framed principal-donor curve and framed Darboux-direction curve. We obtain some relations between the framed curvatures of new defined framed curves and framed curvatures of given framed curve. By using the obtained relationships we give some characterizations for such curves. We also give methods for constructing framed helix and framed slant helix from planar curves.

키워드

과제정보

The authors would like to thank reviewers for their comments and suggestions.

참고문헌

  1. R. L. Bishop, There is more than one way to frame a curve, American Mathematical Monthly 82 (1975), no. 3, 246-251. https://doi.org/10.1080/00029890.1975.11993807
  2. J. H. Choi and Y. H. Kim, Associated curves of a Frenet curve and their applications, Applied Mathematics and Computation 218 (2012), 9116-9124. https://doi.org/10.1016/j.amc.2012.02.064
  3. T. Fukunaga and M. Takahashi, Existence conditions of framed curves for smooth curves, Journal of Geometry 108 (2017), 763-774. https://doi.org/10.1007/s00022-017-0371-5
  4. S. Honda and M. Takahashi, Framed curves in the Euclidean space, Advances in Geometry 16 (2016), no. 3, 265-276. https://doi.org/10.1515/advgeom-2015-0035
  5. S. Honda and M. Takahashi, Bertrand and Mannheim curves of framed curves in the 3-dimensional Euclidean space, Turkish Journal of Mathematics 44 (2020), 883-899. https://doi.org/10.3906/mat-1905-63
  6. T. Korpinar, M. T. Sariaydin, and E. Turhan, Associated curves according to Bishop frame in Euclidean 3-space, Advanced Modelling and Optimization 15 (2013), 713-717.
  7. N. Macit and M. Duldul, Some new associated curves of a Frenet curve in 𝔼3 and 𝔼4, Turkish Journal of Mathematics 38 (2014), 1023-1037. https://doi.org/10.3906/mat-1401-85
  8. N. Macit and M. Duldul, Relatively normal-slant helices lying on a surface and their characterizations, Hacettepe Journal of Mathematics and Statistics 46 (2017), no. 3, 397-408.
  9. O. Z. Okuyucu and M. Canbirdi, Framed slant helices in Euclidean 3-space, Advances in Difference Equations 2021 (2021), Article number 504.
  10. B. Sahiner, Direction curves of tangent indicatrix of a curve, Applied Mathematics and Computation 343 (2019), 273-284. https://doi.org/10.1016/j.amc.2018.09.021
  11. S. Senyurt, D. Canli, and K. H. Ayvaci, Associated curves from a different point of view in E3, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 71 (2022), no. 3, 826-845. https://doi.org/10.31801/cfsuasmas.1026359
  12. Y. Wang, D. Pei, and R. Gao, Generic properties of framed rectifying curves, Mathematics 7 (2019), no. 1, 37.
  13. B. Dogan Yazici, S. Ozkaldi Karakus, and M. Tosun, Framed curves and their applications based on a new differential equation, International Electronic Journal of Geometry 15 (2022), no. 1, 47-56. https://doi.org/10.36890/iejg.875477