| In this paper , we study the harmonic deformation (see 1.4.2 for definition ) of complex structure on Kdhler manifolds , a harmonic deformation that we study is in essence a solution of the following equation systemFor a harmonic deformation we have , it is natural to ask when a harmonic deformation is a harmonic (0,l)-form with value in T(i.e. △ "φ = 0) . We will answer this question in the first part of this paper,we get some conditions which can guarantee a harmonic deformation on certain Kahler manifolds is a harmonic (0,l)-form with value in T.In the sencond part we find some relations between those conditions which is satisfied on these certain Kdhler manifolds and some nature conditions about their curvature .The motivation of this paper is to extent Y.Ouyang's result about the harmonic deformation on CP~n , in [4] he get:Suppose that φ is a Harmonic Deformation on CP~n equipped with Fubini - Study metric.There exists a constant ∈(n) > 0 such that if ||φ||∞< ∈(n),then φ = 0.According to our investigation about the harmonic deformation of complex structure we get the ∈(n) for certain Kdhler manifolds . |
