  The goal of this paper is to compute the zeta function determinant for the
massive Laplacian on Riemann caps (or spherical suspensions). These manifolds
are defined as compact and boundaryless $D-$dimensional manifolds deformed by a
singular Riemannian structure. The deformed spheres, considered previously in
the literature, belong to this class. After presenting the geometry and
discussing the spectrum of the Laplacian, we illustrate a method to compute its
zeta regularized determinant. The special case of the deformed sphere is
recovered as a limit of our general formulas.
