  In this work we analytically obtain the quasinormal spectrum for the
gravitational perturbation on a higher-dimensional generalization of the Nariai
spacetime that is comprised of the direct product of the two-dimensional de
Sitter space with several two-spheres. A key step in order to attain this
result is to use a suitable basis for the angular functions depending on the
rank of the tensorial degree of freedom that one needs to describe. Here we
define such a basis, which is a generalization of the tensor spherical
harmonics that is suited for spaces that are the product of several spaces of
constant curvature.
