E de Birinci Asli Yön Eğrisiyle Elde Edilen A- net Regle Yüzeyler

Bu makalede, 3- boyutlu Öklid uzayında, birinci asli yön eğrisiyle elde edilen A- net regle yüzeylerin yeni bir parametrizasyonu verildi. Daha sonra, bu yüzeylerin ortalama eğriliği ve Gauss eğriliği elde edildi. Sonuç olarak, Anet yüzeylerin ortalama eğriliğe göre karakterizasyonu elde edildi.

A-Net Ruled Surface Which Generated By First Principle Direction Curve In 3 E

In this paper, we give a new parametrization of A- net surface which generated by first principle direction curve Euclidean 3- space 3 E . Then, we obtain mean curvature and Gaussian curvature of this surface. Finally, we characterize A- net surface according to mean curvature in . E 3

___

  • B. Uzunoğlu, I  . Gök and Y. Yaylı, A new approach on curves of constant precession, Applied Mathematic sand Computation, Vol. 275, pp. 317-323, 2016.
  • A. T. Ali, New special curves and their spherical indicatrices, arXiv:0909.2390v1 [math.DG] 13 Sep 2009.
  • A.J. Hanson and H. Ma, Parallel transport approach to curve framing, Tech. Report 425, Computer Science Dept., Indiana Univ., 1995.
  • T. Körpınar, E. Turhan, Parallel Surfaces to Normal Ruled Surfaces of General Helices in the Sol Space , 3 Sol Bol. Soc. Paran. Mat., Vol. 31 No. 2, pp. 245- 253, 2013.
  • B. H. Lavenda, A New Perspective on Relativity: An Odyssey in Non-Euclidean Geometries, World Scientific Publishing Company, 2012.
  • J. A. Galvez, Surfaces of constant curvature in 3- dimensional space forms, Matematica Contemporanea, Vol. 37, pp. 01-42, 2009.
  • S. Izumiya and N. Takeuchi, New special curves and developable surfaces, Turk J. Math., Vol. 28 , pp. 153- 163, 2004.
  • Z. Soyuçok, The Problem of Non- Trivial Isometries of Surfaces Preserving Principal Curvatures, Journal of Geometry, Vol. 52, pp. 173- 188, 1995.
  • A. Bobenko, U. Eitner, Bonnet Surfaces and Painleve Equations, J. Reine Angew Math., Vol. 499, pp. 47- 79, 1998.
  • F. Kanbay, Bonnet Ruled Surfaces, Acta Mathematica Sinica, English Series, Vol. 21 No.3, pp. 623- 630, 2005.
  • F. Kanbay, On the Pairs of Orthogonal Ruled Surfaces, European Journal of Pure and Applied Mathematics, Vol. 5 No. 2, pp. 205-210, 2012.
  • H. Bağdatlı and Z. Soyuçok, On the problem of isometry of a hypersurface preserving mean curvature, Proceedings Mathematical Sciences, Vol. 117 No. 1, pp. 49-59, 2007.
  • J. Oprea, Differential Geometry and its applications, Prentice Hall, 1997.