Non-degenerate homogeneous $$\epsilon $$ ϵ -Kähler and $$\epsilon $$ ϵ -quaternion Kähler structures of linear type

Abstract

We study the class of non-degenerate homogeneous structures of linear type in the pseudo-Kahler, para-Kahler, pseudo-quaternion Kahler and para-quaternion Kahler cases. We show that these structures characterize spaces of constant holomorphic, para-holomorphic, quaternion and para-quaternion sectional curvature respectively. In addition the corresponding homogeneous models are computed, exhibiting the relation between these kind of structures and the incompleteness of the metric.