Corpus ID: 237941145

Triharmonic Curves in f-Kenmotsu Manifolds

  title={Triharmonic Curves in f-Kenmotsu Manifolds},
  author={Serife Nur Bozdag},
  • S. Bozdag
  • Published 27 September 2021
  • Mathematics
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. 
Remarks on polyharmonic curves of constant curvature
In this article we study r-harmonic curves of constant curvature where we mostly focus on the case of curves on the sphere. By performing various explicit calculations for r = 2, 3, 4 we deduceExpand


Triharmonic Curves in 3-Dimensional Homogeneous Spaces
We first prove that, unlike the biharmonic case, there exist triharmonic curves with nonconstant curvature in a suitable Riemannian manifold of arbitrary dimension. We then give the completeExpand
Énergie et déformations en géométrie différentielle
© Annales de l’institut Fourier, 1964, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » ( implique l’accord avec les conditionsExpand
Slant curves in three-dimensional f-Kenmotsu manifolds
Abstract The aim of this paper is to study slant curves of three-dimensional f -Kenmotsu manifolds. These curves are characterized through the scalar product between the normal at the curve and theExpand
On Biharmonic and Biminimal Curves in 3-dimensional f-Kenmotsu Manifolds
In the present paper, we study biharmonicity and biminimality of the curves in 3-dimensional f-Kenmotsu manifolds. We investigate necessary and sufficient conditions for a slant curve in aExpand
k-harmonic maps into a Riemannian manifold with constant sectional curvature
J. Eells and L. Lemaire introduced k-harmonic maps, and Wang Shaobo showed the first variational formula. When, k=2, it is called biharmonic maps (2-harmonic maps). There have been extensive studiesExpand
2-harmonic maps and their first and second variational formulas
In [1], J. Eells and L. Lemaire introduced the notion of a k-harmonic map. In this paper we study the case k = 2, derive the first and second variational formulas of the 2-harmonic maps, giveExpand
Harmonic Maps and Stability on f-Kenmotsu Manifolds
  • V. Mangione
  • Mathematics, Computer Science
  • Int. J. Math. Math. Sci.
  • 2008
The stability of a -holomorphic map from a compact -Kenmotsu manifold to a Kählerian manifold is proven. Expand
Selected topics on harmonic maps
Introduction Part I. Differential geometric aspects of harmonic maps Part II. Problems relating to harmonic maps Bibliography for Part I Supplementary bibliography for Part II.
Contact manifolds in Riemannian geometry
Contact manifolds.- Almost contact manifolds.- Geometric interpretation of the contact condition.- K-contact and sasakian structures.- Sasakian space forms.- Non-existence of flat contact metricExpand
Recently S. Tanno has classified connected almostcontact Riemannian manifolds whose automorphism groups have themaximum dimension [9]. In his classification table the almost contactRiemannianExpand