Homogeneous structures of linear type on $\epsilon$-K\"ahler and $\epsilon$-quaternion K\"ahler manifolds

Abstract

We analyze degenerate homogeneous structures of linear type in the pseudo-K\"ahler and para-K\"ahler cases. The local form and the holonomy of pseudo-K\"ahler or para-K\"ahler manifolds admitting such structure are obtained. In addition the associated homogeneous models are studied exhibiting their relation with the incompleteness of the metric. The same questions are tackled in the pseudo-quaternion K\"ahler and para-quaternion K\"ahler cases. These results complete the study of homogeneous structures of linear type in pseudo-K\"ahler, para-K\"ahler, pseudo-quaternion K\"ahler and para-quaternion K\"ahler cases.