Conformally flat Kaluza-Klein spaces, pseudo-/para-complex space forms and generalized gravitational kinks

The equations describing the Kaluza-Klein reduction of conformally flat spaces are investigated in arbitrary dimensions. Special classes of solution related to pseudo-Kähler and para-Kähler structures are constructed and classified according to spacetime dimension, signature and gauge field rank. Remarkably, rank two solutions include gravitational kinks together with their centripetal and centrifugal deformations.