# On Interpolating Sesqui-Harmonic Legendre Curves in Sasakian Space Forms

## TL;DR

This paper investigates the conditions under which Legendre curves in Sasakian space forms are interpolating sesqui-harmonic, providing theoretical criteria and an explicit example.

## Contribution

It establishes necessary and sufficient conditions for interpolating sesqui-harmonic Legendre curves in Sasakian space forms and presents a concrete example.

## Key findings

- Derived explicit conditions for interpolating sesqui-harmonic Legendre curves.
- Provided an example of such a curve in a Sasakian space form.
- Enhanced understanding of harmonic properties in Sasakian geometry.

## 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.