Finite dimensional JB*-triples have a uniquely associated simply connected
compact symmetric manifold. In infinite dimensions, different constructions
have been used to yield three possibly different Banach manifolds from a J
B*-triple all of which display compact like behaviour. We clarify the relat
ionship between these three manifolds and characterise a case when all thre
e of these manifolds coincide as in the finite dimensional case. These resu
lts have been announced in [11].