E3 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 birparametrizasyonu verildi. Daha sonra, bu yüzeylerin ortalama eğriliği ve Gauss eğriliği elde edildi. Sonuç olarak, Anet yüzeylerin ortalama eğriliğe göre karakterizasyonu elde edildi.

Anahtar Kelimeler:

Regle yüzey, A- net yüzey, birinci asli yön eğrisi, ortalama eğrilik, Gauss eğrilik

A-Net Ruled Surface Which Generated By First Principle Direction Curve In E3

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

Keywords:

Ruled surface, A- net surface, first principle direction curve, mean curvature, Gaussian curvature,

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[1] B. Uzunoğlu, . Gök and Y. Yaylı, A new approach on curves of constant precession, Applied Mathematic sand Computation, vol. 275, pp. 317-323, 2016.
[2] T. A. Ali, New special curves and their spherical indicatrices, arXiv:0909.2390v1 [math.DG] 13 Sep 2009.
[3] A.J. Hanson and H. Ma, Parallel transport approach to curve framing, Tech. Report 425, Computer Science Dept., Indiana Univ., 1995.
[4] T. Körpınar, E. Turhan, Parallel Surfaces to Normal Ruled Surfaces of General Helices in the Sol Space Bol. Soc. Paran. Mat., vol. 2, pp. 245-253, 2013.
[5] B. H. Lavenda, A New Perspective on Relativity: An Odyssey in Non-Euclidean Geometries, 2012.
[6] J. Galvez, Surfaces of constant curvature in 3-dimensional space forms, Matematica Contemporanea, vol. 37, pp. 01-42, 2009.
[7] S. Izumiya and N. Tkeuchi, New special curves and developable surfaces, Turk J. Math., vol. 28, pp. 153-163, 2004.
[8] Z. Soyuçok, The Problem of Non- Trivial Isometries of Surfaces Preserving Principal Curvatures, Journal of Geometry, vol. 52, pp. 173- 188, 1995.
[9] A. Bobenko, U. Either, Bonnet Surfaces and Painleve Equations, J. Reine Angew Math., vol. 499, pp. 47- 79, 1998.
[10] F. Kanbay, Bonnet Ruled Surfaces, Acta Mathematica Sinica, English Series, vol. 21, pp. 623- 630, 2005.