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On the classification of left-invariant para-K\"{a}hler structures on four-dimensional Lie groups by Smolentsev, N. K.; Shagabudinova, I. Y. is a scholarly article available to read on EtoBox.

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

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.

Author

Smolentsev, N. K.; Shagabudinova, I. Y.

Published

2020

Language

EN