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



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Carmona Jiménez, J. L. and Castrillón López, Marco (2020) Reduction of Homogeneous Pseudo-Kähler Structures by One-Dimensional Fibers. Axioms . ISSN 2075-1680

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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.

Item Type:Article
Uncontrolled Keywords:Ambrose–Singer connections; almost contact metric manifolds; homogeneous manifolds; homogeneous structures; pseudo-Kähler manifolds; pseudo-Riemannian metric
Subjects:Sciences > Mathematics > Algebra
ID Code:75547
Deposited On:15 Nov 2022 13:57
Last Modified:16 Nov 2022 08:32

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