Some characterizations of Pseudo-Complex space forms

Abstract

B. Y . Chen and K. Ogiue [2] have proved th a t a K ahler m anifold is a complex space form if and only if it has constant antiholom orphic sectional curvature. In th is note we extend this result to a Pseudo-K ahler manifold and give another characterization of a Pseudo-Complex space form, which m ay be considered as a complex version of the criterian for constancy of sectional curvature of a R iem annian Manifold, ohtained by Cartan [1].