  The real physics meaning of constant k in the Robertson-Walker metric is
discussed when scalar factor R(t) is relative to time. Based on the curvature
formula of the Riemannian geometry strictly, the spatial curvature of the R-W
metric is calculated. The result indicates that the spatial curvature of the
R-W metric is not a constant when R(t) changes with time and the constant in
the R-W metric k does not represent spatial curvature factor. It can only be
considered as an adjustable parameter relative to the Hubble constant. The
result is completely different from the current understanding which is based on
specious estimation actually, in stead of strict calculation. In light of this
result, many conclusions in the current cosmology, such as the values of the
Hubble constant, dark material and dark energy densities, should be
re-estimated. In this way, we may get rid of the current puzzle situation of
cosmology thoroughly.
