  We construct an anti-de-Sitter (AdS) geometry from a conformal field theory
(CFT) defined on a general conformally flat manifold via a flow equation
associated with the curved manifold, which we refer to as the primary flow
equation. We explicitly show that the induced metric associated with the
primary flow equation becomes AdS whose boundary is the curved manifold.
Interestingly, it turns out that such an AdS metric with conformally flat
boundary is obtained from the usual Poincare AdS by a simple bulk
diffeomorphism transformation. We also demonstrate that the emergence of such
an AdS space is guaranteed only by the conformal symmetry at boundary, which
converts to the AdS isometry after quantum averaging, as in the case of the
flat boundary.
