Equitorsion holomorphically projective mappings of generalized m-parabolic Kähler manifolds

Abstract

We investigate equitorsion holomorphically projective mappings of generalized m-parabolic Kähler manifolds and provide some necessary and sufficient conditions for the existence of these mappings in form of linear PDE-systems. Also, we find an invariant geometric object with respect to a holomorphically projective mapping of generalized m-parabolic Kähler manifolds which is analogous to the Thomas projective parameter. Definition 1.1. [18]A generalized Riemannian manifold (M, ) of even dimension n (n > 2) is said to be a generalized m-parabolic Kähler manifold if there exists a tensor field F on M of type (1, 1) such that rank(F) = m ≤ n 2 and the following conditions hold

Generalized para-Kähler spaces in Eisenhart’s sense admitting a holomorphically projective mapping

“…In this subsection we shall consider holomorphically projective mappings between generalized para-Kähler spaces preserving the torsion tensor, i.e., so called equitorsion holomorphically projective mappings [16]. Equitorsion holomorphically projective mappings were firstly considered between generalized Kähler spaces [15,28,29] and later between generalized hyperbolic and m-parabolic Kähler spaces [16,20].…”

“…By using the fact that the torsion tensor T 1 and the structure F are preserved under an equitorsion holomorphically projective mapping and by substituting (21) and (22) into (20) we obtain that…”

Fundamental theorems of quasi-geodesic mappings of generalized-recurrent-parabolic spaces

“…The studied mappings are holomorphically projective mappings between parabolic Kähler spaces. These problems were studied in [4,17,21,22] and also in the dissertation by Shiha [25].…”