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On the Construction of the Surface Family with a Common Involute Geodesic

Yıl 2023, Cilt: 11 Sayı: 2, 162 - 168, 31.10.2023

Öz

In this study, we produce a surface family possessing an involute of a given curve as a geodesic. We find necessary and sufficient conditions for the given curve such that its involute is a geodesic on any member of the surface family. Also, we present important results for ruled and developable surfaces. Finally, we present two examples to support our results.

Kaynakça

  • [1] J. McCleary Geometry from a differentiable viewpoint. Cambridge University Press, 1995.
  • [2] G.J. Wang, K. Tang and C.L.Tai, Parametric representation of a surface pencil with a common spatial geodesic, Comput. Aided Des., 36(5) (2004), 447-459.
  • [3] E. Kasap, F.T. Akyıldız and K. Orbay, A generalization of surfaces family with common spatial geodesic, Appl. Math. Comput., 201 (2008), 781–789.
  • [4] E. Kasap, F.T. Akyildiz, Surfaces with common geodesic in Minkowski 3-space, Appl. Math. Comput., 177 (2006), 260-270.
  • [5] G. S¸ affak, E. Kasap, Family of surface with a common null geodesic. Int. J. Phys. Sci., 4(8) (2009), 428-433.
  • [6] G. S¸ affak, E. Kasap, Surfaces family with common null asymptotic. Appl. Math. Comput. 260 (2015), 135139.
  • [7] C.Y. Li, R.H. Wang, C.G. Zhu, Parametric representation of a surface pencil with a common line of curvature. Comput. Aided Des. 43(9) (2011) 1110–1117.
  • [8] Bayram E., G¨uler F., Kasap E. Parametric representation of a surface pencil with a common asymptotic curve. Comput. Aided Des. 44, 637-643, 2012.
  • [9] E. Bayram, M. Bilici, Surface family with a common involute asymptotic curve, International Journal of Geometric Methods in Modern Physics, 13(5) (2016), 1650062.
  • [10] E. Erg¨un, E. Bayram, E. Kasap, Surface pencil with a common line of curvature in Minkowski 3-space. Acta Math. Sinica, English Series. 30(12) (2014), 2103-2118.
  • [11] M.P. do Carmo, Differential geometry of curves and surfaces. Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1976.
  • [12] Hsiung CC. A first course in differential geometry. John Wiley & Sons Inc., USA, 1981.
  • [13] J. Oprea, Differential geometry and its applications. Pearson Education Inc., USA, 2007.
  • [14] M. C¸ alıs¸kan, M. Bilici, Some characterizations for the pair of involute-evolute curves in Euclidean space E3. Bull. of Pure and App. Sci., 21E(2) (2002), 289-294.
  • [15] M. Bilici, E. Bayram, Surface construction with a common involute line of curvature, Int. J. Open Problems Compt. Math, 14(2) (2021), 20-31.
  • [16] S. Senyurt, S. Sivas and A. C¸ alıs¸kan, NC Smarandache curves of involute evolute curve couple according to Frenet frame algebras, Groups And Geometries, 33(2) (2016), 153-164.
  • [17] S. Kılıc¸o˘glu, S. Senyurt and A. C¸ alıskan, On the tangent vector fields of striction curves along the involute and Bertrandian Frenet ruled surfaces, International J. Math. Combin, 2 (2018), 33-43.
  • [18] K. Eren, K. Yesmakhanova, S. Ersoy and R. Myrzakulov, Involute evolute curve family induced by the coupled dispersionless equations. Optik, 270 (2022), 169915.
  • [19] M. Bilici, S. Palavar, New-type tangent indicatrix of involute and ruled surface according to Blaschke frame in dual space, Maejo Int. J. Sci. Technol., 16(3) (2022), 199-207.
  • [20] S. Sivas, S. Senyurt and A. C¸ alıskan, Smarandache curves of involute-evolute curve According to Frenet Frame, Fundam. Contemp. Math. Sci. , 4(1) (2023), 31-45.
  • [21] M. Bilici, A Survey on Timelike-spacelike involute-evolute curve pair, Erzincan University J. Sci. Technol., 16 (1) (2023), 49-57 .
  • [22] M. Bilici, A new method for designing involute trajectory timelike ruled surfaces in Minkowski 3-space, Bol. da Soc. Parana. de Mat., 41 (2023), 1-11.
  • [23] G. K¨oseo˘glu, M. Bilici, Involutive sweeping surfaces with Frenet frame in Euclidean 3-space, HELIYON, 9(8) (2023), e18822.
  • [24] M. Bilici, G. K¨oseo˘glu, Tubular involutive surfaces with Frenet frame in Euclidean 3-space, Maejo Int. J. Sci. Technol., 17(2) (2023), 96-106.
Yıl 2023, Cilt: 11 Sayı: 2, 162 - 168, 31.10.2023

Öz

Kaynakça

  • [1] J. McCleary Geometry from a differentiable viewpoint. Cambridge University Press, 1995.
  • [2] G.J. Wang, K. Tang and C.L.Tai, Parametric representation of a surface pencil with a common spatial geodesic, Comput. Aided Des., 36(5) (2004), 447-459.
  • [3] E. Kasap, F.T. Akyıldız and K. Orbay, A generalization of surfaces family with common spatial geodesic, Appl. Math. Comput., 201 (2008), 781–789.
  • [4] E. Kasap, F.T. Akyildiz, Surfaces with common geodesic in Minkowski 3-space, Appl. Math. Comput., 177 (2006), 260-270.
  • [5] G. S¸ affak, E. Kasap, Family of surface with a common null geodesic. Int. J. Phys. Sci., 4(8) (2009), 428-433.
  • [6] G. S¸ affak, E. Kasap, Surfaces family with common null asymptotic. Appl. Math. Comput. 260 (2015), 135139.
  • [7] C.Y. Li, R.H. Wang, C.G. Zhu, Parametric representation of a surface pencil with a common line of curvature. Comput. Aided Des. 43(9) (2011) 1110–1117.
  • [8] Bayram E., G¨uler F., Kasap E. Parametric representation of a surface pencil with a common asymptotic curve. Comput. Aided Des. 44, 637-643, 2012.
  • [9] E. Bayram, M. Bilici, Surface family with a common involute asymptotic curve, International Journal of Geometric Methods in Modern Physics, 13(5) (2016), 1650062.
  • [10] E. Erg¨un, E. Bayram, E. Kasap, Surface pencil with a common line of curvature in Minkowski 3-space. Acta Math. Sinica, English Series. 30(12) (2014), 2103-2118.
  • [11] M.P. do Carmo, Differential geometry of curves and surfaces. Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1976.
  • [12] Hsiung CC. A first course in differential geometry. John Wiley & Sons Inc., USA, 1981.
  • [13] J. Oprea, Differential geometry and its applications. Pearson Education Inc., USA, 2007.
  • [14] M. C¸ alıs¸kan, M. Bilici, Some characterizations for the pair of involute-evolute curves in Euclidean space E3. Bull. of Pure and App. Sci., 21E(2) (2002), 289-294.
  • [15] M. Bilici, E. Bayram, Surface construction with a common involute line of curvature, Int. J. Open Problems Compt. Math, 14(2) (2021), 20-31.
  • [16] S. Senyurt, S. Sivas and A. C¸ alıs¸kan, NC Smarandache curves of involute evolute curve couple according to Frenet frame algebras, Groups And Geometries, 33(2) (2016), 153-164.
  • [17] S. Kılıc¸o˘glu, S. Senyurt and A. C¸ alıskan, On the tangent vector fields of striction curves along the involute and Bertrandian Frenet ruled surfaces, International J. Math. Combin, 2 (2018), 33-43.
  • [18] K. Eren, K. Yesmakhanova, S. Ersoy and R. Myrzakulov, Involute evolute curve family induced by the coupled dispersionless equations. Optik, 270 (2022), 169915.
  • [19] M. Bilici, S. Palavar, New-type tangent indicatrix of involute and ruled surface according to Blaschke frame in dual space, Maejo Int. J. Sci. Technol., 16(3) (2022), 199-207.
  • [20] S. Sivas, S. Senyurt and A. C¸ alıskan, Smarandache curves of involute-evolute curve According to Frenet Frame, Fundam. Contemp. Math. Sci. , 4(1) (2023), 31-45.
  • [21] M. Bilici, A Survey on Timelike-spacelike involute-evolute curve pair, Erzincan University J. Sci. Technol., 16 (1) (2023), 49-57 .
  • [22] M. Bilici, A new method for designing involute trajectory timelike ruled surfaces in Minkowski 3-space, Bol. da Soc. Parana. de Mat., 41 (2023), 1-11.
  • [23] G. K¨oseo˘glu, M. Bilici, Involutive sweeping surfaces with Frenet frame in Euclidean 3-space, HELIYON, 9(8) (2023), e18822.
  • [24] M. Bilici, G. K¨oseo˘glu, Tubular involutive surfaces with Frenet frame in Euclidean 3-space, Maejo Int. J. Sci. Technol., 17(2) (2023), 96-106.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Mustafa Bilici 0000-0002-3502-5027

Ergin Bayram 0000-0003-2633-0991

Yayımlanma Tarihi 31 Ekim 2023
Gönderilme Tarihi 19 Mart 2022
Kabul Tarihi 21 Eylül 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 11 Sayı: 2

Kaynak Göster

APA Bilici, M., & Bayram, E. (2023). On the Construction of the Surface Family with a Common Involute Geodesic. Konuralp Journal of Mathematics, 11(2), 162-168.
AMA Bilici M, Bayram E. On the Construction of the Surface Family with a Common Involute Geodesic. Konuralp J. Math. Ekim 2023;11(2):162-168.
Chicago Bilici, Mustafa, ve Ergin Bayram. “On the Construction of the Surface Family With a Common Involute Geodesic”. Konuralp Journal of Mathematics 11, sy. 2 (Ekim 2023): 162-68.
EndNote Bilici M, Bayram E (01 Ekim 2023) On the Construction of the Surface Family with a Common Involute Geodesic. Konuralp Journal of Mathematics 11 2 162–168.
IEEE M. Bilici ve E. Bayram, “On the Construction of the Surface Family with a Common Involute Geodesic”, Konuralp J. Math., c. 11, sy. 2, ss. 162–168, 2023.
ISNAD Bilici, Mustafa - Bayram, Ergin. “On the Construction of the Surface Family With a Common Involute Geodesic”. Konuralp Journal of Mathematics 11/2 (Ekim 2023), 162-168.
JAMA Bilici M, Bayram E. On the Construction of the Surface Family with a Common Involute Geodesic. Konuralp J. Math. 2023;11:162–168.
MLA Bilici, Mustafa ve Ergin Bayram. “On the Construction of the Surface Family With a Common Involute Geodesic”. Konuralp Journal of Mathematics, c. 11, sy. 2, 2023, ss. 162-8.
Vancouver Bilici M, Bayram E. On the Construction of the Surface Family with a Common Involute Geodesic. Konuralp J. Math. 2023;11(2):162-8.
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