On the classification of left-invariant para-Kähler structures on four-dimensional Lie groups

N. K. Smolentsev; I. Y. Shagabudinova

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arXiv · 2008.05664

On the classification of left-invariant para-Kähler structures on four-dimensional Lie groups

N. K. Smolentsev·I. Y. Shagabudinova

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Abstract

A first classification of para-Kähler structures on four-dimensional Lie algebras was obtained by D. Calvaruzo in 2015. In this paper, we propose another classification based on the classification of symplectic Lie algebras. For each four-dimensional symplectic Lie algebra, compatible para-complex structures and the corresponding pseudo-Riemannian metrics are found in explicit form. This leads to the classification of Sasaki para-contact structures on five-dimensional contact Lie algebras with a nontrivial center.

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N. K. Smolentsev, I. Y. Shagabudinova. 2020-08-13. On the classification of left-invariant para-Kähler structures on four-dimensional Lie groups. https://arxiv.org/abs/2008.05664

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