  Motivated by recent studies on the uniqueness or non-uniqueness of higher
dimensional black hole spacetime, we investigate the asymptotic structure of
spatial infinity in n-dimensional spacetimes($n \geq 4$). It turns out that the
geometry of spatial infinity does not have maximal symmetry due to the
non-trivial Weyl tensor {}^{(n-1)}C_{abcd} in general. We also address static
spacetime and its multipole moments P_{a_1 a_2 ... a_s}. Contrasting with four
dimensions, we stress that the local structure of spacetimes cannot be unique
under fixed a multipole moments in static vacuum spacetimes. For example, we
will consider the generalized Schwarzschild spacetimes which are deformed black
hole spacetimes with the same multipole moments as spherical Schwarzschild
black holes. To specify the local structure of static vacuum solution we need
some additional information, at least, the Weyl tensor {}^{(n-2)}C_{abcd} at
spatial infinity.
