Generalized para-Kähler 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-Kähler 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 mappings between generalized para-Kähler 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 projective curvature tensor in case of holomorphically projective mappings between usual para-Kähler spaces. dl(t) dt 0, t ∈ I, is said to be a holomorphically planar curve if for some functions ρ 1 and ρ 2 of a parameter t the following ordinary differential equation holds [27, 30] ∇ λ(t) λ(t) = ρ 1 (t)λ(t) + ρ 2 (t)Fλ(t),

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