Publication Details:
Journal or Publication Title:
Armenian Journal of Mathematics=Հայկական մաթեմատիկական հանդես
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Title:
Biharmonic Helices in Three-Dimensional Lorentzian Egorov and ε-Spaces
Creator:
Fatima Zahra Benzahra-Belkacem ; Noura Sidhoumi
Contributor(s):
Գլխ. խմբ.՝ Անրի Ներսեսյան ; Պատ. խմբ.՝ Լինդա Խաչատրյան ; Խմբ. տեղակալ՝ Ռաֆայել Բարխուդարյան
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Uncontrolled Keywords:
Biharmonic Curves ; Frenet-Serre ; Equations ; Torsion
Coverage:
Abstract:
We consider three-dimensional Lorentzian Egorov and ε -spaces and show that the existence of proper biharmonic helices in these manifolds is highly constrained and closely tied to the causal character of the Frenet frame. In particular, we prove that no proper biharmonic helices exist in Egorov spaces unless the space is flat and the normal vector is spacelike. Furthermore, we establish that no proper biharmonic helices exist in three-dimensional ε -spaces.
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General note:
Electronic Open Access Publication of the National Academy of Sciences of Armenia