Abstract
We use the tangential component psi(T) of an immersion of a compact hypersurface of the Euclidean space Em+1 in finding two characterizations of a sphere. In first characterization, we use psi(T) as a geodesic vector field (vector field with all its trajectories geodesics) and in the second characterization, we use psi(T) to annihilate the de-Rham Laplace operator on the hypersurface.