Volume 4, Issue 1-2, January 2015, Page: 19-23
On the Explicit Parametric Equation of a General Helix with First and Second Curvature in Nil 3-Space
Şeyda Kılıçoğlu, Faculty of Education, Department of Elementary Mathematics Education, Baskent University, Ankara, Turkey
Received: Nov. 21, 2014;       Accepted: Nov. 24, 2014;       Published: Jan. 12, 2015
DOI: 10.11648/j.pamj.s.2015040102.15      View  2921      Downloads  168
Abstract
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 [12], in Nil 3-Space.
Keywords
Nil Space, Helix, Curvatures
To cite this article
Şeyda Kılıçoğlu, 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. doi: 10.11648/j.pamj.s.2015040102.15
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