Laplacian Conditions and Sphericity of Hypersurfaces in the Nearly Kähler 6-Sphere

In this paper, we investigate hypersurfaces in the nearly Kähler 6-sphere S6 and establish several foundational results. In particular, under certain conditions of the function ξ(f)=g(∇f,ξ), we demonstrate that a hypersurface M of S6 must be a sphere. Here, f∈C∞(M) is a smooth vector field, ξ=−JN denotes the characteristic vector field, J is the almost complex structure on S6, and N is the unit vector field normal to the hypersurface. We also support our results with illustrative examples.