GEOMETRY OF THE RICCI SOLITON HYPERSURFACES
In this paper, we investigate the geometry of the Ricci soliton hypersurface in a Euclidean space. We find sufficient conditions first for this Ricci soliton hypersurface to be totally geodesic and to be isometric to a sphere. We also study two special cases, when the mean curvature is a constant and when the scalar curvature is a constant.
Ricci soliton, hypersurfaces, Euclidean spaces, Ricci operator, scalar curvature.