Left-invariant almost para-K\"{a}hler structures on six-dimensional nilpotent Lie groups

Nikolay K. Smolentsev

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arXiv · 2208.06755

Left-invariant almost para-K\"{a}hler structures on six-dimensional nilpotent Lie groups

Nikolay K. Smolentsev

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Abstract

In this paper, we consider left-invariant para-complex structures on six-dimensional nilpotent Lie groups. A complete list of six-dimensional nilpotent Lie groups that admit para-K\"{a}hler structures is obtained, explicit expressions for para-complex structures are found, and curvature properties of associated para-K\"{a}hler metrics are investigated. It is shown that paracomplex structures are nilpotent and the corresponding para-K\"{a}hler metrics are Ricci-flat.

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BibTeX RIS

Nikolay K. Smolentsev. 2022-08-14. Left-invariant almost para-K\"{a}hler structures on six-dimensional nilpotent Lie groups. https://arxiv.org/abs/2208.06755

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