We define under which circumstances two multi-warped product spacetimes can
be considered equivalent and then we classify the spaces of constant curvature
in the Euclidean and Lorentzian signature. For dimension D=2, we get
essentially twelve representations, for D=3 exactly eighteen. More general, for
every even D, 5D+2 cases exist, whereas for every odd D, 5D+3 cases exist. For
every D, exactly one half of them has the Euclidean signature. Our definition
is well suited for the discussion of multidimensional cosmological models, and
our results give a simple algorithm to decide whether a given metric represents
the inflationary de Sitter spacetime (in unusual coordinates) or not.Comment: 21 pages, LaTeX, no figures, J. Math. Phys. in prin