  It is known that supersymmetric nonlinear sigma models for the compact Kahler
manifolds G/H cannot be consistently coupled to supergravity, since the Kahler
potentials are not invariant under the G transformation. We show that the
supersymmetric nonlinear sigma models can be deformed such that the Kahler
potential be exactly G-invariant if and only if one enlarges the manifolds by
dropping all the U(1)'s in the unbroken subgroup H. Then, those nonlinear sigma
models can be coupled to supergravity without losing the G invariance.
