The paper gives a method to generate the potential functions which can induce Khler metrics u=uij dz idz j of Bergman type on the unit ball B n in C n.The paper proves that if h∈C n(B n)is harmonic in these metrics u...The paper gives a method to generate the potential functions which can induce Khler metrics u=uij dz idz j of Bergman type on the unit ball B n in C n.The paper proves that if h∈C n(B n)is harmonic in these metrics u(u h=0)in B n,then h must be pluriharmonic in B n.In fact,it is a characterization theorem,as a consequence,the paper provides a way to construct many counter examples for the potential functions of the metric u so that the above theorem fails.The results in this paper generalize the theorems of Graham(1983)and examples constructed by Graham and Lee(1988).展开更多
文摘The paper gives a method to generate the potential functions which can induce Khler metrics u=uij dz idz j of Bergman type on the unit ball B n in C n.The paper proves that if h∈C n(B n)is harmonic in these metrics u(u h=0)in B n,then h must be pluriharmonic in B n.In fact,it is a characterization theorem,as a consequence,the paper provides a way to construct many counter examples for the potential functions of the metric u so that the above theorem fails.The results in this paper generalize the theorems of Graham(1983)and examples constructed by Graham and Lee(1988).
