MATHEMATICS

Left-invariant para-Kähler structures on six-dimensional nilpotent Lie groups

N. K. Smolentsev

Kemerovo State University, Kemerovo, Russian Federation

Abstract: Left-invariant para-complex structures on six-dimensional nilpotent Lie groups are considered. A complete list of six-dimensional nilpotent Lie groups that admit para-Kähler structures is obtained, explicit expressions for para-complex structures are found, and curvature properties of associated para-Kähler metrics are investigated. It is shown that paracomplex structures are nilpotent and the corresponding para-Kähler metrics are Ricci-flat.

Keywords: six-dimensional nilpotent Lie groups, symplectic Lie groups, para-complex structures, left-invariant para-Kahler structures.

UDC: 514.76

MSC: 53C15, 53D10, 53C25, 53C50

Received: 02.12.2021
Accepted: July 12, 2022

DOI: 10.17223/19988621/78/3

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