  In a noncompact harmonic manifold $M$ we establish finite dimensionality of
the eigenspaces $V_{\lambda}$ generated by radial eigenfunctions of the form
$\cosh r + c$. As a consequence, for such harmonic manifolds, we give an
isometric imbedding of $M$ into $(V_{\lambda},B)$, where $B$ is a nondegenerate
symmetric bilinear indefinite form on $V_{\lambda}$ (analogous to the imbedding
of the real hyperbolic space $I\!\!\!H^{n}$ into $I\!\!\!R^{n+1}$ with the
indefinite form $Q(x,x) = -x_0^2 + \sum x_i^2$). Finally we give certain
conditions under which $M$ is symmetric.
