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.
Highlights
Ambrose and Singer [1] gave a tensorial approach to study homogeneous Riemannian manifolds by the so-called homogeneous structure S
Homogeneous manifolds are a central object for many mathematical models of physical theories
We show that the almost contact metric manifold is of type C5 ⊕ C6 ⊕ C7 ⊕ C8 ⊕ C9 ⊕ C10 ⊕ C12 of Chinea-González classification
Summary
Ambrose and Singer [1] gave a tensorial approach to study homogeneous Riemannian manifolds by the so-called homogeneous structure S. Homogeneous manifolds are a central object for many mathematical models of physical theories (for example, linear degenerate homogeneous structures are related to homogeneous plane waves; cf [6]). This is specially relevant when the space is equipped with additional geometry, such as contact or Kähler. As the homogeneous structures of almost contact metric manifolds are related with the covariant derivative of the fundamental 2-form associated to it, we prove that the reduced manifold by a homogeneous linear structure is of type.
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