The Infinitesimal Holomorphically Projective Deformations of Special Parabolically Kahlerian Spaces

Abstract

We present the most important concepts related to the research: Kahler parabolic space, the holomorphic curve and the projective holomorphic mapping, then define the infinitesimal deformations between Kahler parabolic spaces and the infinitesimally projective holomorphic deformations in Kahler parabolic spaces, and we also find the necessary and sufficient conditions for the Kahler parabolic space  to be a non- trivially deformation holomorphic projective. Then we study the infinitesimally projective holomorphic deformation of semi- symmetric and symmetric Kahler parabolic spacesand affine equal Kahler parabolic spaces.