A New Type of Generalized Para-Kahler Spaces and Holomorphically Projective Transformations

In the present paper, we define a new class of generalized para-Kahler spaces by using two different kinds of covariant derivatives. Some properties of the curvature tensors as well as those of the corresponding Ricci tensors of new generalized para-Kahler spaces are pointed out. Also, we consider some tensor fields that are invariant with respect to holomorphically projective mappings of generalized para-Kahler spaces. Finally, we examine some PDE systems for the existence of infinitesimal holomorphically projective transformations of new types of generalized para-Kahler spaces with parallel torsion.