Abstract
In this paper, we study inverse curves of general helices in the Sol³. Finally, we find out explicit parametric equations of inverse curves in the Sol³.
Highlights
An inversion with respect to the sphere SC (r) with the center C ∈ Sol3 is given by r2 P −C
We denote that Sol3 ∗ = Sol3 − {C}
(3.4) and (3.7) is illustrated in Fig.2: Figure 2: Parametric equations for Eqs
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Summary
Introduction
3. Inverse Curves of General Helices in Sol Space Sol3 The Frenet frame satisfies the following Frenet–Serret equations: With respect to the orthonormal basis {e1, e2, e3}, we can write The parametric equations of γ are x (s) sin Pe− C21 +
Results
Conclusion
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