Research Article
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Tubular Surfaces According to a Focal Curve in E^3

Year 2023, Volume: 15 Issue: 2, 433 - 442, 31.12.2023

Abdullah Yıldırım

https://doi.org/10.47000/tjmcs.1092714

Abstract

A spine curve moves through the middle of a canal or a tubular surface. It might be asked whether it is possible to carry a spine curve over a tubular surface. For a tubular surface, we have seen that it can be done. In this study, we have given the general equations of a canal surface and a tubular surface according to a focal curve. In this case, we found the fundamental curvatures of a tubular surface. We gave theorems and proofs about the focal curve being a special curve.

Keywords

Focal curve tube surface parameric curve geodesic

References

  • Alegre, P., Arslan, K., Carriazo, A., Murathan, C., Öztürk, G., Some special types of developable rued surface, Hacettepe Journal of Mathematics and Statistics, 39(3)(2010), 319–325.
  • Doğan, F., Yaylı, Y., On the curvatures of the tubular surface with Bishop , Commun. Fac. Sci. Univ. Ank. Series A1, 60(1)(2011), 59–69.
  • Öztürk, G., Arslan, K., On focal curves in Euclidean n-space Rn, Novi Sad J. Math, 46(1)(2016), 35-44.
  • Hacısalihoğlu, H.H., Differensiyel Geometri Cilt II, Hacısalihoğlu Yayınları, Ankara, 2000.
  • Karacan, M.K., Bukcu, B., An alternative moving frame for tubular surfaces around spacelike curves with a spacelike Binormal in the Minkowski 3-space, Mathematica Moravica, 12(2)(2007), 47–54.
  • Monterde, J., Salkowski curves revised: A family of curves with constant curvature and non-constant torsion, Computer Aided Geometric Design, 26(3)(2009), 271–278.
  • Oprea, J., Differential Geometry and Its Applications, Prentice-Hall Inc., New Jersey, 1997.
  • Özdemir, M., Ergin, A.A., Spacelike Darboux curves in Minkowski 3-space, Differential Geometry-Dynamical Systems, 9(2007), 131–137.
  • Saffak, A.G., Ayvacı, K.H., Surface family with a common Mannheim-B isogeodesic curve, Balkan Journal of Geometry and Its Applications, 26(2)2021, 1–12.
  • Şenyurt, S., Ayvacı, K.H., Canlı, D., Family of Surfaces with a Common Special Involute and Evolute Curves, Internatıonal Electronıc Journal of Geometry,15(1)2022, 160–174.
  • Uribe-Vargas, R., On vertices focal curvatures and differential geometry of space curves, Bull. Brazilian Math. Soc., 36(3)(2005), 285–307.
  • Yıldırım, A., Tubular surface around a Legendre curve in BCV spaces, New Trends in Mathematical Sciences, 4(2)(2016), 61–71.

Year 2023, Volume: 15 Issue: 2, 433 - 442, 31.12.2023

Abdullah Yıldırım

https://doi.org/10.47000/tjmcs.1092714

Abstract

References

  • Alegre, P., Arslan, K., Carriazo, A., Murathan, C., Öztürk, G., Some special types of developable rued surface, Hacettepe Journal of Mathematics and Statistics, 39(3)(2010), 319–325.
  • Doğan, F., Yaylı, Y., On the curvatures of the tubular surface with Bishop , Commun. Fac. Sci. Univ. Ank. Series A1, 60(1)(2011), 59–69.
  • Öztürk, G., Arslan, K., On focal curves in Euclidean n-space Rn, Novi Sad J. Math, 46(1)(2016), 35-44.
  • Hacısalihoğlu, H.H., Differensiyel Geometri Cilt II, Hacısalihoğlu Yayınları, Ankara, 2000.
  • Karacan, M.K., Bukcu, B., An alternative moving frame for tubular surfaces around spacelike curves with a spacelike Binormal in the Minkowski 3-space, Mathematica Moravica, 12(2)(2007), 47–54.
  • Monterde, J., Salkowski curves revised: A family of curves with constant curvature and non-constant torsion, Computer Aided Geometric Design, 26(3)(2009), 271–278.
  • Oprea, J., Differential Geometry and Its Applications, Prentice-Hall Inc., New Jersey, 1997.
  • Özdemir, M., Ergin, A.A., Spacelike Darboux curves in Minkowski 3-space, Differential Geometry-Dynamical Systems, 9(2007), 131–137.
  • Saffak, A.G., Ayvacı, K.H., Surface family with a common Mannheim-B isogeodesic curve, Balkan Journal of Geometry and Its Applications, 26(2)2021, 1–12.
  • Şenyurt, S., Ayvacı, K.H., Canlı, D., Family of Surfaces with a Common Special Involute and Evolute Curves, Internatıonal Electronıc Journal of Geometry,15(1)2022, 160–174.
  • Uribe-Vargas, R., On vertices focal curvatures and differential geometry of space curves, Bull. Brazilian Math. Soc., 36(3)(2005), 285–307.
  • Yıldırım, A., Tubular surface around a Legendre curve in BCV spaces, New Trends in Mathematical Sciences, 4(2)(2016), 61–71.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Abdullah Yıldırım 0000-0002-6579-3799

Publication Date December 31, 2023
Published in Issue Year 2023 Volume: 15 Issue: 2

Cite

APA Yıldırım, A. (2023). Tubular Surfaces According to a Focal Curve in E^3. Turkish Journal of Mathematics and Computer Science, 15(2), 433-442. https://doi.org/10.47000/tjmcs.1092714
AMA Yıldırım A. Tubular Surfaces According to a Focal Curve in E^3. TJMCS. December 2023;15(2):433-442. doi:10.47000/tjmcs.1092714
Chicago Yıldırım, Abdullah. “Tubular Surfaces According to a Focal Curve in E^3”. Turkish Journal of Mathematics and Computer Science 15, no. 2 (December 2023): 433-42. https://doi.org/10.47000/tjmcs.1092714.
EndNote Yıldırım A (December 1, 2023) Tubular Surfaces According to a Focal Curve in E^3. Turkish Journal of Mathematics and Computer Science 15 2 433–442.
IEEE A. Yıldırım, “Tubular Surfaces According to a Focal Curve in E^3”, TJMCS, vol. 15, no. 2, pp. 433–442, 2023, doi: 10.47000/tjmcs.1092714.
ISNAD Yıldırım, Abdullah. “Tubular Surfaces According to a Focal Curve in E^3”. Turkish Journal of Mathematics and Computer Science 15/2 (December 2023), 433-442. https://doi.org/10.47000/tjmcs.1092714.
JAMA Yıldırım A. Tubular Surfaces According to a Focal Curve in E^3. TJMCS. 2023;15:433–442.
MLA Yıldırım, Abdullah. “Tubular Surfaces According to a Focal Curve in E^3”. Turkish Journal of Mathematics and Computer Science, vol. 15, no. 2, 2023, pp. 433-42, doi:10.47000/tjmcs.1092714.
Vancouver Yıldırım A. Tubular Surfaces According to a Focal Curve in E^3. TJMCS. 2023;15(2):433-42.