Legendre surfaces with harmonic mean curvature vector field in the unit 5-sphere

TL;DR

This paper derives explicit formulas for Legendre surfaces in the 5-sphere that have a harmonic mean curvature vector field, assuming the mean curvature is constant along a specific direction.

Contribution

It provides the first explicit representation of such Legendre surfaces with harmonic mean curvature in the 5-sphere under a specific constancy condition.

Findings

Explicit representation formulas for the surfaces.

Conditions for harmonic mean curvature vector fields.

Characterization of surfaces with constant mean curvature along a direction.

Abstract

We obtain the explicit representation of Legendre surfaces in the unit $5$-sphere with harmonic mean curvature vector field, under the condition that the mean curvature function is constant along a certain special direction.