Global geometric properties of AdS space and the AdS/CFT correspondence

The Poisson kernels and relations between them for a massive scaler field i n a unit ball B-n with Hua's metric and conformal flat metric are obtained by describing the B-n as a submanifold of an (n + 1)-dimensional embedding space. Global geometric properties of the AdS space are discussed. We show that the (n + 1)-dimensional AdS space AdS(n+1) is isomorphic to RP1 x B-n and boundary of the AdS is isomorphic to RP1 x Sn-1. Bulk-boundary propagat or and the AdS/CFT like correspondence are demonstrated based on these glob al geometric properties of the RP1 x B-n.