Non-relativity of K\"ahler manifold and complex space forms

We study the non-relativity for two real analytic K\"ahler manifolds and complex space forms of three types. The first one is a K\"ahler manifold whose polarization of local K\"ahler potential is a Nash function in a local coordinate. The second one is the Hartogs domain equpped with two canonical metrics whose polarizations of the K\"ahler potentials are the diastatic functions.