Complete hypersurfaces with $w$-constant mean curvature in the unit spheres

. In this paper, we study 4-dimensional complete hypersurfaces with w -constant mean curvature in the unit sphere. We give a lower bound of the scalar curvature for 4-dimensional complete hypersurfaces with w -constant mean curvature. As a by-product, we give a new proof of the result of Deng-Gu-Wei [10] under the weaker topological condition.