  We solve the Einstein equations in higher dimensions with warped geometry
where an extra dimension is assumed to have orbifold symmetry $S^{1}/Z_{2}$.
The setup considered here is an extension of the five-dimensional
Randall-Sundrum model to $5+D$ dimensions, and hidden and observable branes are
fixed on the orbifold. It is assumed that the brane tension (self-energy) of
each brane with $(4+D)$-dimensional spacetime is anisotropic and that the
warped metric function of the four dimensions is generally different from that
of the extra $D$ dimensions. We point out that the forms of the warped metric
functions and the relations between the tensions of two branes depend on the
integration constant appearing in the Einstein equations as well as on the sign
of the bulk cosmological constant.
