Abstract
We define generalized hyperbolic Kähler spaces as a particular case of Eisenhart's generalized Riemannian spaces, with some additional conditions related to the almost product structure. Since a generalized hyperbolic Kähler space is equipped with a non-symmetric basic tensor, it admits five linearly independent curvature tensors. Some properties of these curvature tensors as well as those of the corresponding Ricci tensors are established. Also, we consider holomorphically projective mappings, as well as equitorsion holomorphically projective mappings between generalized hyperbolic Kähler spaces and find some invariant geometric objects with respect to these mappings.
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