Reduction of Homogeneous Pseudo-Kähler Structures by One-Dimensional Fibers

Abstract

We study the reduction procedure applied to pseudo-Kähler manifolds by a one dimensional Lie group acting by isometries and preserving the complex tensor. We endow the quotient manifold with an almost contact metric structure. We use this fact to connect pseudo-Kähler homogeneous structures with almost contact metric homogeneous structures. This relation will have consequences in the class of the almost contact manifold. Indeed, if we choose a pseudo-Kähler homogeneous structure of linear type, then the reduced, almost contact homogeneous structure is of linear type and the reduced manifold is of type C5⊕C6⊕C12 of Chinea-González classification.

Keywords

• Ambrose–Singer connections
• almost contact metric manifolds
• homogeneous manifolds
• homogeneous structures
• pseudo-Kähler manifolds
• pseudo-Riemannian metrics