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Tubular Surfaces According to a Focal Curve in E^3

Yıl 2023, Cilt: 15 Sayı: 2, 433 - 442, 31.12.2023

Abdullah Yıldırım

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

Öz

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.

Anahtar Kelimeler

Focal curve tube surface parameric curve geodesic

Kaynakça

  • 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.

Yıl 2023, Cilt: 15 Sayı: 2, 433 - 442, 31.12.2023

Abdullah Yıldırım

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

Öz

Kaynakça

  • 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.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Abdullah Yıldırım 0000-0002-6579-3799

Yayımlanma Tarihi 31 Aralık 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 15 Sayı: 2

Kaynak Göster

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. Aralık 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, sy. 2 (Aralık 2023): 433-42. https://doi.org/10.47000/tjmcs.1092714.
EndNote Yıldırım A (01 Aralık 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, c. 15, sy. 2, ss. 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 (Aralık 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, c. 15, sy. 2, 2023, ss. 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.