On the Explicit Parametric Equation of a General Helix with First and Second Curvature in Nil 3-Space
Pure and Applied Mathematics Journal
Volume 4, Issue 1-2, January 2015, Pages: 19-23
Received: Nov. 21, 2014;
Accepted: Nov. 24, 2014;
Published: Jan. 12, 2015
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Şeyda Kılıçoğlu, Faculty of Education, Department of Elementary Mathematics Education, Baskent University, Ankara, Turkey
Nil geometry is one of the eight geometries of Thurston's conjecture. In this paper we study in Nil 3-space and the Nil metric with respect to the standard coordinates (x,y,z) is gNil₃=(dx)²+(dy)²+(dz-xdy)² in IR³. In this paper, we find out the explicit parametric equation of a general helix. Further, we write the explicit equations Frenet vector fields, the first and the second curvatures of general helix in Nil 3-Space. The parametric equation the Normal and Binormal ruled surface of general helix in Nil 3-space in terms of their curvature and torsion has been already examined in , in Nil 3-Space.
On the Explicit Parametric Equation of a General Helix with First and Second Curvature in Nil 3-Space, Pure and Applied Mathematics Journal. Special Issue: Applications of Geometry.
Vol. 4, No. 1-2,
2015, pp. 19-23.
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