We examine some of the implications of implementing the usual boundary
conditions on the closed bosonic string in the hamiltonian framework. Using the
KN formalism, it is shown that at the quantum level, the resulting constraints
lead to relations among the periods of the basis 1-forms. These are compared
with those of Riemanns' which arise from a different consideration.Comment: 16 pages, (Plain Tex), NUS/HEP/9320