Complex Projective Space And Multi-ring Surface Harmonic Deformation

Complex projective space CP~n is a compact complex analytic manifold of dimension n,and a K'dhler manifold and equipped with Fubini — Study metric(this is K'dhler metric). φ is a (0,1) form with values in T(Let T be its holomorphic tangent bundle).If φ is a harmonic deformation on CP~n ,satisfies:Complex trous is also a compact complex manifold,there is a constant coefficient K'dhler metric.If ψ is a harmonic deformation on CT~n and also satisfies the above three conditions.In this paper,We use Bochner's technology ,that to say ,evaluate curvature and estimate it,we get the theorem as follows,Th3.1 Suppose that φ is a harmonic deformation on CP~n,if Th4.1 Suppose that ψ is a harmonic deformation on CT~n,if || ψ ||∞< ,then It's a true harmonic deformation.