Holomorphically Projective Mappings of (Pseudo-) K¨ahler Manifolds Preserve the Class of Dierentiability

Abstract

In this paper we study fundamental equations  of holomorphically projective mappings of (pseudo-) K\"ahler manifolds  with respect to the smoothness class of metrics $C^r$, $r\geq1$.
 We show that holomorphically projective mappings preserve the smoothness class of metrics.