On the classification of left-invariant para-K\"{a}hler structures on four-dimensional Lie groups

13 Aug 2020  ·  Smolentsev N. K., Shagabudinova I. Y. ·

A first classification of para-K\"{a}hler 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. read more

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Differential Geometry