Revista Matemática Iberoamericana


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Volume 33, Issue 1, 2017, pp. 139–168
DOI: 10.4171/RMI/930

Published online: 2017-02-22

Homogeneous structures of linear type on $\epsilon$-Kähler and $\epsilon$-quaternion Kähler manifolds

Marco Castrillón López[1] and Ignacio Luján[2]

(1) Universidad Complutense de Madrid, Spain
(2) Universidad Complutense de Madrid, Spain

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.

Keywords: Homogeneous plane waves, para-Kähler, pseudo-Kähler, pseudo-quaternion Kähler, para-quaternion Kähler, reductive homogeneous pseudo-Riemannian spaces

Castrillón López Marco, Luján Ignacio: Homogeneous structures of linear type on $\epsilon$-Kähler and $\epsilon$-quaternion Kähler manifolds. Rev. Mat. Iberoamericana 33 (2017), 139-168. doi: 10.4171/RMI/930