On interpolating sesqui-harmonic Legendre curves in Sasakian space forms

Abstract

We consider interpolating sesqui-harmonic Legendre curves in Sasakian space forms. We find the necessary and sufficient conditions for Legendre curves in Sasakian space forms to be interpolating sesqui-harmonic. Finally, we obtain an example for an interpolating sesqui-harmonic Legendre curve in a Sasakian space form.Mathematics Subject Classification. 53C25, 53C40, 53A05.

Interpolating sesqui harmonic slant curve in generalized Sasakian space form

“…In particular we give an example of interpolating sesqui-harmonic slant curve in Sasakian space form. Our paper generalizes the results of the papers [8,16,20].and characterized by the vanishing of bi-tension field τ 2 (π) = tr(∇ π ∇ π − ∇ π ∇ )τ(π) − tr(R N (dπ, τ(π))dπ) = 0.…”

A Note on Generalized Sasakian Space Forms with Interpolating Sesqui-Harmonic Legendre Curves

“…For Case I and Case VI, using Theorem 3.2 and Theorem 3.7, then we obtain the following result in [10]: (1) γ is interpolating sesqui-harmonic with δ1 δ2 = 0 if and only if it is a Legendre circle with k 1 = 1 − δ1 δ2 where 1 > δ1 δ2 ; or…”

“…In [5], the same author studied a conservation law and used it to show the smoothness of weak solutions for a spherical target and found several classification results for interpolating sesqui-harmonic maps. In [10], the author, Özgür and De studied interpolating sesqui-harmonic Legendre curves in Sasakian space forms. In [16], Özgür and Güvenç studied biharmonic Legendre curves in generalized Sasakian space forms.…”

“…[10]Let (N 2n+1 , φ, ξ, η, g) be a Sasakian space form with c = 1 or φT ⊥ E 2 and γ : I ⊂ R −→ N 2n+1 a Legendre curve of osculating order r.…”

Sesqui-Harmonic Curves in LP-Sasakian Manifolds

“…In a 3-dimensional sphere, interpolating sesqui-harmonic curves were studied in [3]. Interpolating sesqui-harmonic Legendre curves in Sasakian space forms were characterized in [5]. Recently, Yüksel Perktaş et all.…”