Non-relativity of Kähler manifold and complex space forms

We study the non-relativity for two real analytic Kähler manifolds and complex space forms of three types. The first one is a Kähler manifold whose polarization of local Kähler 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 Kähler potentials are the diastatic functions.

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