Holomorphically projective mappings between generalized hyperbolic Kähler spaces

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].…”

“…In the present paper we provide a more general definition of generalized para-Kähler spaces in Eisenhart's sense than the one given in [16]. These results as well as those concerning F-planar mappings given in [21] are included in the author's Ph.D. thesis [19].…”

“…We should note that investigation of special Eisenhart's generalized Riemannian spaces and their diffeomorphisms is an active research topic [32][33][34][35][36]. A kind of generalized hyperbolic Kähler spaces and holomorphically projective mappings between these spaces were considered in [16]. On the other hand we gave a more general definition of generalized Kähler spaces in Eisenhart's sense [22].…”

“…for arbitrary vector fields X and Y, i.e., condition (3) is fulfilled. The previous discussion leads to the more general definition of generalized para-Kähler spaces than the one given in [16].…”

Equitorsion holomorphically projective mappings of generalized m-parabolic Kähler manifolds

“…Minčć [10-14, 21, 26]. Further, generalized elliptic, hyperbolic and parabolic Kählerian spaces were developed in [14,[17][18][19][20]26]. Recently, generalized m-parabolic Kähler manifolds were defined in [18].…”