  Analysis of the WKB exactness in some homogeneous spaces is attempted. $CP^N$
as well as its noncompact counterpart $D_{N,1}$ is studied. $U(N+1)$ or U(N,1)
based on the Schwinger bosons leads us to $CP^N$ or $D_{N,1}$ path integral
expression for the quantity, ${\rm tr} e^{-iHT}$, with the aid of coherent
states. The WKB approximation terminates in the leading order and yields the
exact result provided that the Hamiltonian is given by a bilinear form of the
creation and the annihilation operators. An argument on the WKB exactness to
more general cases is also made.
