On the General Helix with First and Second Curvature in Nil 3-Space | Chapter 9 | Recent Advances in Mathematical Research and Computer Science Vol. 10

Thurston's conjecture has eight geometries, one of which is nil geometry. In geometry, the helix, null helix, and slant helix have been studied in the publications [1], [2], and [3, respectively. The Nil metric with respect to the standard coordinates (x,y,z) is gNil3=(dx)2+(dy)2+(dz-xdy)2 in IR3, which we investigate in Nil 3-space. This paper contains the explicit parametric equation for a generic helix. The explicit equations Frenet vector fields, the first and second curvatures of the generic helix are likewise expressed in Nil 3-Space. [4] has already investigated the parametric equation of the Normal and Binormal governed surface of general helix in terms of curvature and torsion in Nil 3-space.

Author(s) Details:

Seyda Kilicoglu,
Department of Elementary Mathematics Education, Faculty of Education, Baskent University, Ankara, Turkey.

Please see the link here: https://stm.bookpi.org/RAMRCS-V10/article/view/6277