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Characteristic properties of the parallel ruled surfaces with Darboux frame in Euclidean 3- space

Year 2016, Volume: 1 Issue: 1, 26 - 43, 01.01.2016

Yasin Unluturk , Muradiye Cimdiker Cumali Ekici

Abstract

In this paper, the parallel ruled surfaces with Darboux frame are introduced in Euclidean 3-space. Then some characteristic
properties such as developability, striction point and distribution parameter of the parallel ruled surfaces with Darboux frame are given
in Euclidean 3-space. Then we obtain Steiner rotation vector of this kind of surfaces Euclidean 3-space. By using this rotation vector,
we compute pitch length and pitch angle of the parallel ruled surfaces with Darboux frame. 

Keywords

Parallel ruled surface Darboux frame developability Steiner rotation vector pitch length pitch angle.

References

  • Aydemir, I. & Kasap, E. 2005. Timelike ruled surface with spacelike rulings in R. Kuwait Journal of Science & Engineering 32(2): 13-24.
  • C¸ oken, A.C., C¸ iftc¸i, ¨ U. & Ekici, C. 2008. On parallel timelike ruled surfaces with timelike rulings. Kuwait Journal of Science & Engineering 35(1): 21-31.
  • Darboux, G. 1896. Lec¸ons sur la theorie generale des surfaces I-II-III-IV., Gauthier-Villars, Paris.
  • Gray, A., Salamon, S. & Abbena, E. 2006. Modern differential geometry of curves and surfaces with Mathematica. Chapman and Hall/CRC.
  • Hacısalihoglu, H. H. 1983. Diferensiyel geometri. Inonu Univ. Fen Edebiyat Fak. Yay. No.2.
  • Hlavaty, V. 1945. Differentielle linien geometrie. Uitg P. Noorfhoff, Groningen.
  • Hoschek, J. 1973. Integral invarianten von regelflachen. Arch. Math, XXIV.
  • Karadag, H. B., Kılıc¸, E. & Karadag, M. 2014. On the developable ruled surfaces kinematically generated in Minkowski 3-Space. Kuwait Journal of Science 41(1): 21-34.
  • Kuhnel, W. 2002. Differential geometry, curves-surfaces-manifolds. American Mathematical Society. ¨
  • Muller, H. R. 1978. Verallgemeinerung einer formelvon Steiner. Abh. Braunschweig Wiss. Ges. 31:107-113, 1978.
  • O’Neill, B. 1996. Elementary differential geometry. Academic Press Inc, New York.
  • Ravani, T. & Ku S. 1991. Bertrand offsets of ruled surface and developable surface. Comp Aided Geom Design 23(2):145-152.
  • Savcı, Z. 2011. On parallel ruled Weingarten surfaces in 3-dimensional Euclidean space. (in Turkish) PhD Thesis, Eskisehir Osmangazi Univ. Grad. Sch. Nat. Sci., Eskisehir.
  • Senturk, G. Y. & Y ¨ uce, S. 2015. Characteristic properties of the ruled surface with Darboux frame in E3. Kuwait Journal of Science, 42(2):14-33.
  • Senturk, G. Y. & Y ¨ uce, S. 2015a. Properties of integral invariants of the involute-evolute offsets of ruled surfaces. Int. J. Pure Appl. Math. 102(4):757-768.
  • Unluturk, Y. & Ekici, C. 2014. Parallel surfaces satisying the properties of ruled surfaces in Minkowski 3-space. Global Journal of Science Frontier Research F, 14(1):78-95.

Year 2016, Volume: 1 Issue: 1, 26 - 43, 01.01.2016

Yasin Unluturk , Muradiye Cimdiker Cumali Ekici

Abstract

References

  • Aydemir, I. & Kasap, E. 2005. Timelike ruled surface with spacelike rulings in R. Kuwait Journal of Science & Engineering 32(2): 13-24.
  • C¸ oken, A.C., C¸ iftc¸i, ¨ U. & Ekici, C. 2008. On parallel timelike ruled surfaces with timelike rulings. Kuwait Journal of Science & Engineering 35(1): 21-31.
  • Darboux, G. 1896. Lec¸ons sur la theorie generale des surfaces I-II-III-IV., Gauthier-Villars, Paris.
  • Gray, A., Salamon, S. & Abbena, E. 2006. Modern differential geometry of curves and surfaces with Mathematica. Chapman and Hall/CRC.
  • Hacısalihoglu, H. H. 1983. Diferensiyel geometri. Inonu Univ. Fen Edebiyat Fak. Yay. No.2.
  • Hlavaty, V. 1945. Differentielle linien geometrie. Uitg P. Noorfhoff, Groningen.
  • Hoschek, J. 1973. Integral invarianten von regelflachen. Arch. Math, XXIV.
  • Karadag, H. B., Kılıc¸, E. & Karadag, M. 2014. On the developable ruled surfaces kinematically generated in Minkowski 3-Space. Kuwait Journal of Science 41(1): 21-34.
  • Kuhnel, W. 2002. Differential geometry, curves-surfaces-manifolds. American Mathematical Society. ¨
  • Muller, H. R. 1978. Verallgemeinerung einer formelvon Steiner. Abh. Braunschweig Wiss. Ges. 31:107-113, 1978.
  • O’Neill, B. 1996. Elementary differential geometry. Academic Press Inc, New York.
  • Ravani, T. & Ku S. 1991. Bertrand offsets of ruled surface and developable surface. Comp Aided Geom Design 23(2):145-152.
  • Savcı, Z. 2011. On parallel ruled Weingarten surfaces in 3-dimensional Euclidean space. (in Turkish) PhD Thesis, Eskisehir Osmangazi Univ. Grad. Sch. Nat. Sci., Eskisehir.
  • Senturk, G. Y. & Y ¨ uce, S. 2015. Characteristic properties of the ruled surface with Darboux frame in E3. Kuwait Journal of Science, 42(2):14-33.
  • Senturk, G. Y. & Y ¨ uce, S. 2015a. Properties of integral invariants of the involute-evolute offsets of ruled surfaces. Int. J. Pure Appl. Math. 102(4):757-768.
  • Unluturk, Y. & Ekici, C. 2014. Parallel surfaces satisying the properties of ruled surfaces in Minkowski 3-space. Global Journal of Science Frontier Research F, 14(1):78-95.
There are 16 citations in total.

Details

Journal Section Mathematics, Engineering and statistics
Authors

Yasin Unluturk

Muradiye Cimdiker This is me

Cumali Ekici This is me

Publication Date January 1, 2016
Published in Issue Year 2016 Volume: 1 Issue: 1

Cite

APA Unluturk, Y., Cimdiker, M., & Ekici, C. (2016). Characteristic properties of the parallel ruled surfaces with Darboux frame in Euclidean 3- space. Communication in Mathematical Modeling and Applications, 1(1), 26-43.
AMA Unluturk Y, Cimdiker M, Ekici C. Characteristic properties of the parallel ruled surfaces with Darboux frame in Euclidean 3- space. CMMA. January 2016;1(1):26-43.
Chicago Unluturk, Yasin, Muradiye Cimdiker, and Cumali Ekici. “Characteristic Properties of the Parallel Ruled Surfaces With Darboux Frame in Euclidean 3- Space”. Communication in Mathematical Modeling and Applications 1, no. 1 (January 2016): 26-43.
EndNote Unluturk Y, Cimdiker M, Ekici C (January 1, 2016) Characteristic properties of the parallel ruled surfaces with Darboux frame in Euclidean 3- space. Communication in Mathematical Modeling and Applications 1 1 26–43.
IEEE Y. Unluturk, M. Cimdiker, and C. Ekici, “Characteristic properties of the parallel ruled surfaces with Darboux frame in Euclidean 3- space”, CMMA, vol. 1, no. 1, pp. 26–43, 2016.
ISNAD Unluturk, Yasin et al. “Characteristic Properties of the Parallel Ruled Surfaces With Darboux Frame in Euclidean 3- Space”. Communication in Mathematical Modeling and Applications 1/1 (January 2016), 26-43.
JAMA Unluturk Y, Cimdiker M, Ekici C. Characteristic properties of the parallel ruled surfaces with Darboux frame in Euclidean 3- space. CMMA. 2016;1:26–43.
MLA Unluturk, Yasin et al. “Characteristic Properties of the Parallel Ruled Surfaces With Darboux Frame in Euclidean 3- Space”. Communication in Mathematical Modeling and Applications, vol. 1, no. 1, 2016, pp. 26-43.
Vancouver Unluturk Y, Cimdiker M, Ekici C. Characteristic properties of the parallel ruled surfaces with Darboux frame in Euclidean 3- space. CMMA. 2016;1(1):26-43.