Generalized para-K\"ahler spaces in Eisenhart's sense admitting a holomorphically projective mapping

Abstract

We relax the conditions related to the almost product structure and in such a way introduce a wider class of generalized para-K\"ahler spaces.
Some properties of the curvature tensors as well as those of the corresponding Ricci tensors of these spaces are pointed out.
We consider holomorphically projective (HP) mappings between generalized para-K\"ahler spaces in Eisenhart's sense.
Also, we examine some invariant geometric objects with respect to equitorsion holomorphically projective mappings.
These geometric objects reduce to the para-holomorphic curvature tensor in case of HP mappings between usual para-K\"ahler spaces.