It is known that to any Riemannian manifold (M, g ), with or without boundary, one can associate certain fundamental objects. Among them are the Laplace-Beltrami opera- tor and the Hodge-de Rham operators, which are natural that is, they commute with the isometries of (M, g)], elliptic, self-adjoint second order differential operators acting on the space of real valued smooth functions on M and the spaces of smooth differential forms on M, respectively...