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…
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March 29, 2022 0