  This paper shows that the Grassmann Manifolds $G_{\bf F}(n,N)$ can all be
imbedded in an Euclidean space $M_{\bf F}(N)$ naturally and the imbedding can
be realized by the eigenfunctions of Laplacian $\triangle$ on $G_{\bf F}(n,N)$.
They are all minimal submanifolds in some spheres of $M_{\bf F}(N)$
respectively. Using these imbeddings, we construct some degenerate Morse
functions on Grassmann Manifolds, show that the homology of the complex and
quaternion Grassmann Manifolds can be computed easily.
