2021/09/27 by Şerife Nur Bozdağ, Serife Nur Bozdag, Bozdag, Serife Nur
Mathematics · #53C25 #53C43 #58E20 #Computer science #Constant (computer programming) #Curvature #Differential Geometry (math.DG) #FOS: Mathematics #Frenet–Serret formulas #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry #Geometry and complex manifolds #Legendre polynomials #Mathematical analysis #Mathematics #math.DG #msc:53C25 #msc:53C43 #msc:58E20
paper · pdf · doi:10.48550/arxiv.2109.13034
14 pages
arxiv created 2021/09/27 · openalex publication_date 2021/09/27 · arxiv updated 2021/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.