Abstract
In this paper, parallel surfaces to normal ruled surface of general helices in the Sol³ are studied. Also, explicit parametric equations of parallel surfaces to normal ruled surface of general helices in the Sol³ are found.
Highlights
General Helices in Sol Space Sol3Assume that {T, N, B} be the Frenet frame field along γ
Ez dx, ω e−z dy, ω dz, and the orthonormal basis dual to the 1-forms is e1
Proof: It is obvious from Theorem 4.2
Summary
Assume that {T, N, B} be the Frenet frame field along γ. The Frenet frame satisfies the following Frenet–Serret equations:. ( [14]) Let γ : I −→ Sol[3] be a unit speed non-geodesic general helix. The parametric equations of γ are sin Pe− cos Ps−C3 x (s) =. Z (s) = cos Ps + C3, where C1, C2, C3, C4, C5 are constants of integration. Parallel Surfaces to Normal Ruled Surfaces of General Helices in Sol[3]. The purpose of this section is to study parallel surfaces to normal ruled surfaces of general helices in Sol[3]. Let γ : I −→ Sol[3] is a unit speed non-geodesic general helix in Sol[3]. The equation of normal ruled surface of γ is
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