Triharmonic Curves in f-Kenmotsu Manifolds
Serife Nur Bozdag
TL;DR
This paper explores the properties of triharmonic curves in three-dimensional f-Kenmotsu manifolds, providing conditions for their existence and characterizing certain types of these curves.
Contribution
It establishes necessary and sufficient conditions for triharmonic Frenet, slant, and Legendre curves, and proves nonexistence of triharmonic Legendre curves in this setting.
Findings
Frenet curves with constant curvature are helices.
No triharmonic Legendre curves exist in three-dimensional f-Kenmotsu manifolds.
Conditions for slant and Frenet curves to be triharmonic are derived.
Abstract
The aim of this paper is to study triharmonic curves in three dimensional f-Kenmotsu manifolds. We investigate necessary and sufficient conditions for Frenet curves, and specifically for slant and Legendre curves to be triharmonic. Then we prove that triharmonic Frenet curves with constant curvature are Frenet helices in three dimensional f-Kenmotsu manifolds. Next, we give a nonexistence theorem that there is no triharmonic Legendre curve in three dimensional f-Kenmotsu manifolds.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Geometric and Algebraic Topology