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ON RULED NON-DEGENERATE SURFACES WITH DARBOUX FRAME IN MINKOWSKI 3-SPACE

Yıl 2020, Cilt: 10 Sayı: 2, 499 - 511, 01.03.2020

Öz

In this paper, ruled non-degenerate surfaces with respect to Darboux frame are studied. Characterization of them which are related to the geodesic torsion, the normal curvature and the geodesic curvature with respect to Darboux frame are examined. Furthermore, some special cases of non-null rulings are demonstrated according to Frenet frame {T, N, B} with Darboux frame {T, g, n}. Finally, the integral invariants of these surfaces are examined.

Kaynakça

  • Ravani, B. and Ku, T. S., (1991), Bertrand offsets of ruled and developable surfaces, Comp. Aided. Geom. Design., 23 (2), pp. 145–152.
  • Turgut, A. and Hacısaliho˘glu, H. H., (1997), Spacelike ruled surfaces in the Minkowski 3-space, Com- mun. Fac. Sci. Univ. Ank. Series A1, 46, pp. 83–91.
  • Turgut, A. and Hacısaliho˘glu, H. H., (1998), Timelike ruled surfaces in the Minkowski 3-space-II, Turkish J. Math., 1, pp. 33–46.
  • Turgut, A. and Hacısaliho˘glu, H. H., (1997), On the distribution parameter of timelike ruled surfaces in the Minkowski 3-space, Far East Journal of Mathematical Sciences 5(2), pp. 321–328.
  • Kim, Y. H. and Yoon, D. W., (2004), Classification of ruled surfaces in Minkowski 3-spaces, Journal of Geometry and Physics, 49(1), pp.89–100.
  • Kasap, E. and Kuruo˘glu, N., (2006), The Bertrand offsets of ruled surfaces in R3, Acta Math. Viet- nam., 31, pp. 39–48.
  • Kim, Y. H. and Yoon, D. W., (2007), On non-developable ruled surfaces in Lorentz-Minkowski 3- spaces, Taiwanese Journal of Mathematics, 11(1), pp. 197–214.
  • Kasap, E., Y¨uce, S. and Kuruo˘glu, N., (2009), The involute-evolute offsets of ruled surfaces, Iranian
  • J. Sci. Tech. Transaction A, 33, pp. 195–201. Orbay, K., Kasap, E. and Aydemir, ˙I., (2009), Mannheim offsets of ruled surfaces, Math. Problems
  • Engineering, Article Id 16091.
  • Y¨uksel, N., (2013), The Ruled Surfaces According to Bishop Frame in Minkowski 3-Space, Abstract and Applied Analysis, Article ID 810640.
  • Ekici,C. and ¨Ozt¨urk, H., (2013), On time-like ruled surfaces in Minkowski 3-space, Universal Journal of Applied Science, 1, pp. 56–63.
  • Kızıltu˘g, S. and C¸ akmak, A., (2013), Developable ruled surfaces with Darboux Frame in Minkowski space, Life Science Journal, 10(4), pp. 1906–1914.
  • S¸ent¨urk, G. Y. and Y¨uce, S., (2015), Characteristic properties of the ruled surface with Darboux
  • Frame in E, Kuwait J. Sci. 42(2), pp. 14–33. S¸ent¨urk, G. Y. and Y¨uce, S., (2017), Bertrand offsets of ruled surfaces with Darboux Frame, Results in Mathematics, 72(3), pp. 1151—1159.
  • Yoon, D. W., (2016), On the evolute offsets of ruled surfaces in Minkowski 3-space, Turkish J. Math., , pp. 594–604.
  • O’Neill, B., (1983), Semi-Riemannian Geometry, Academic Press, New York-London.
  • Ratcliffe, J. G., (2006), Foundations of Hyperbolic Manifolds, Graduate Texts in Mathematics, Springer.
  • Akutagawa, K. and Nishikawa, S., (1990), The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space, Tohoku Math. J., 42(1), pp. 67–82.
  • U˘gurlu, H. H., (1997), On the geometry of timelike surfaces, Commun. Fac. Sci. Univ. Ank. Series A1, 46, pp. 211–223.
  • U˘gurlu, H. H. and Kocayi˘git, H., (1996), The Frenet and Darboux Instantaneous Rotation Vectors of
  • Curves on Timelike Surface, Mathematical Computational Applications, 1(2), pp. 131—141. Whittemore, J. K., (1940), Bertrand curves and helices, Duke Math. J., 6, pp. 235–245.
  • L`opez, R., (2008), Differential Geometry of Curves and Surfaces in Lorentz-Minkowski Space, arxiv:0810.3351v1 [math.DG].
Yıl 2020, Cilt: 10 Sayı: 2, 499 - 511, 01.03.2020

Öz

Kaynakça

  • Ravani, B. and Ku, T. S., (1991), Bertrand offsets of ruled and developable surfaces, Comp. Aided. Geom. Design., 23 (2), pp. 145–152.
  • Turgut, A. and Hacısaliho˘glu, H. H., (1997), Spacelike ruled surfaces in the Minkowski 3-space, Com- mun. Fac. Sci. Univ. Ank. Series A1, 46, pp. 83–91.
  • Turgut, A. and Hacısaliho˘glu, H. H., (1998), Timelike ruled surfaces in the Minkowski 3-space-II, Turkish J. Math., 1, pp. 33–46.
  • Turgut, A. and Hacısaliho˘glu, H. H., (1997), On the distribution parameter of timelike ruled surfaces in the Minkowski 3-space, Far East Journal of Mathematical Sciences 5(2), pp. 321–328.
  • Kim, Y. H. and Yoon, D. W., (2004), Classification of ruled surfaces in Minkowski 3-spaces, Journal of Geometry and Physics, 49(1), pp.89–100.
  • Kasap, E. and Kuruo˘glu, N., (2006), The Bertrand offsets of ruled surfaces in R3, Acta Math. Viet- nam., 31, pp. 39–48.
  • Kim, Y. H. and Yoon, D. W., (2007), On non-developable ruled surfaces in Lorentz-Minkowski 3- spaces, Taiwanese Journal of Mathematics, 11(1), pp. 197–214.
  • Kasap, E., Y¨uce, S. and Kuruo˘glu, N., (2009), The involute-evolute offsets of ruled surfaces, Iranian
  • J. Sci. Tech. Transaction A, 33, pp. 195–201. Orbay, K., Kasap, E. and Aydemir, ˙I., (2009), Mannheim offsets of ruled surfaces, Math. Problems
  • Engineering, Article Id 16091.
  • Y¨uksel, N., (2013), The Ruled Surfaces According to Bishop Frame in Minkowski 3-Space, Abstract and Applied Analysis, Article ID 810640.
  • Ekici,C. and ¨Ozt¨urk, H., (2013), On time-like ruled surfaces in Minkowski 3-space, Universal Journal of Applied Science, 1, pp. 56–63.
  • Kızıltu˘g, S. and C¸ akmak, A., (2013), Developable ruled surfaces with Darboux Frame in Minkowski space, Life Science Journal, 10(4), pp. 1906–1914.
  • S¸ent¨urk, G. Y. and Y¨uce, S., (2015), Characteristic properties of the ruled surface with Darboux
  • Frame in E, Kuwait J. Sci. 42(2), pp. 14–33. S¸ent¨urk, G. Y. and Y¨uce, S., (2017), Bertrand offsets of ruled surfaces with Darboux Frame, Results in Mathematics, 72(3), pp. 1151—1159.
  • Yoon, D. W., (2016), On the evolute offsets of ruled surfaces in Minkowski 3-space, Turkish J. Math., , pp. 594–604.
  • O’Neill, B., (1983), Semi-Riemannian Geometry, Academic Press, New York-London.
  • Ratcliffe, J. G., (2006), Foundations of Hyperbolic Manifolds, Graduate Texts in Mathematics, Springer.
  • Akutagawa, K. and Nishikawa, S., (1990), The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space, Tohoku Math. J., 42(1), pp. 67–82.
  • U˘gurlu, H. H., (1997), On the geometry of timelike surfaces, Commun. Fac. Sci. Univ. Ank. Series A1, 46, pp. 211–223.
  • U˘gurlu, H. H. and Kocayi˘git, H., (1996), The Frenet and Darboux Instantaneous Rotation Vectors of
  • Curves on Timelike Surface, Mathematical Computational Applications, 1(2), pp. 131—141. Whittemore, J. K., (1940), Bertrand curves and helices, Duke Math. J., 6, pp. 235–245.
  • L`opez, R., (2008), Differential Geometry of Curves and Surfaces in Lorentz-Minkowski Space, arxiv:0810.3351v1 [math.DG].
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

G. Y. Şentürk

S. Yüce Bu kişi benim

Yayımlanma Tarihi 1 Mart 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 10 Sayı: 2

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