On the General Helix with First and Second Curvature in Nil 3-Space

¬†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

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