Abstract
In this paper, we study biharmonic constant Π₁- slope curves according to type-2 Bishop frame in the SOL³. We characterize the biharmonic constant Π₁- slope curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric integral equations in the SOL³.
Highlights
Integral Equations of Biharmonic Constant Π1− Slope Curves where (x, y, z) are the standard coordinates in R3
Biharmonic Constant Π1−Slope Curves according to New Type-2 Bishop Frame in Sol Space SOL3
Bishop curvatures are defined by k1 = κ(s) cos U (s), k2 = κ(s) sin U (s)
Summary
Integral Equations of Biharmonic Constant Π1− Slope Curves where (x, y, z) are the standard coordinates in R3. We can take the following orthonormal basis {E1, E2, E3} of sol[3] Left-translating the basis {E1, E2, E3}, we obtain the following orthonormal frame field: e1 For the covariant derivatives of the Levi-Civita connection of the left-invariant metric gSOL3 , defined above the following is true: 3. Biharmonic Constant Π1−Slope Curves according to New Type-2 Bishop Frame in Sol Space SOL3
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