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.

中文翻译：

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广义概Hermitian空间和全纯射影映射

我们推导了广义的近似埃尔米特空间的一些有趣的性质。此外，我们研究了广义Kähler空间之间全纯射影映射的基本方程，并研究了两个非线性PDE系统的映射关系。在等值全同射影映射的情况下，我们将那些非线性PDE系统转换为线性PDE系统。允许等价全同射影映射和变换的某些新型广义Kähler空间被定义为线性PDE系统自然存在的结果，因为它们存在这些微分。我们的考虑提供了新的结果，以及先前在几篇论文中发表的一些结果的扩展和改进。