Generalized Almost Hermitian Spaces and Holomorphically Projective Mappings

We derive some interesting properties of generalized almost Hermitian spaces. Additionally, we study basic equations of holomorphically projective mappings between generalized Kähler spaces and examine two non-linear PDE systems for the existence of these mappings. In the case of an equitorsion holomorphically projective mapping, we transform those non-linear PDE-systems into linear PDE systems. Some new types of generalized Kähler spaces that admit equitorsion holomorphically projective mappings and transformations are defined as a natural consequence of the linear PDE systems for the existence of these diffeomorphisms. Our consideration provides new results as well as extensions and improvements of some results previously published in several papers.