Holomorphically projective mappings between generalized m-parabolic Kähler manifolds

Abstract

Generalized m-parabolic K?hler manifolds are defined and holomorphically projective mappings between such manifolds have been considered. Two non-linear systems of PDE?s in covariant derivatives of the first and second kind for the existence of such mappings are given. Also, relations between five linearly independent curvature tensors of generalized m-parabolic K?hler manifolds with respect to these mappings are examined. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 174012]

Equitorsion holomorphically projective mappings of generalized m-parabolic Kähler manifolds

“…A diffeomorphism f : M → M of generalized m-parabolic Kähler manifolds (M, , F) and (M, , F) is said to be an equitorsion HP mapping if it preserves holomorphically planar curves and the torsion tensor [18,20,26]. In this section we give necessary and sufficient conditions for the existence of an equitorsion HP mapping in terms of the symmetric part of the metric and the covariant derivatives of the first and second kind with respect to (w.r.t.)…”

“…A necessary and sufficient condition for the existence of a HP mapping f : M → M between generalized m-parabolic Kähler manifolds M and M is given by [18]…”

“…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].…”

“…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]. We will transform necessary and sufficient conditions for the existence of equitorsion HP mappings of generalized m-parabolic Kähler manifolds from the paper [18] into linear PDE-systems.…”

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

“…On the other hand we gave a more general definition of generalized Kähler spaces in Eisenhart's sense [22]. In the same manner generalized m-parabolic Kähler spaces were defined in [17,18]. A new type of generalized para-Kähler space is given in [23].…”