Homogeneous structures of linear type on -Kähler and -quaternion Kähler manifolds

  • Marco Castrillón López

    Universidad Complutense de Madrid, Spain
  • Ignacio Luján

    Universidad Complutense de Madrid, Spain

Abstract

We analyze degenerate homogeneous structures of linear type in the pseudo-Kähler and para-Kähler cases. The local form and the holonomy of pseudo-Kähler or para-Kähler 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 Kähler and para-quaternion Kähler cases. These results complete the study of homogeneous structures of linear type in pseudo-Kähler, para-Kähler, pseudo-quaternion Kähler and para-quaternion Kähler cases.

Cite this article

Marco Castrillón López, Ignacio Luján, Homogeneous structures of linear type on -Kähler and -quaternion Kähler manifolds. Rev. Mat. Iberoam. 33 (2017), no. 1, pp. 139–168

DOI 10.4171/RMI/930