On left-invariant semi-K\"{a}hler structures on six-dimensional nilpotent nonsymplectic Lie groups

TL;DR

This paper investigates semi-Kähler and almost para-semi-Kähler structures on six-dimensional nilpotent Lie groups that lack symplectic structures but admit complex structures, exploring their geometric properties.

Contribution

It introduces and studies semi-Kähler and almost para-semi-Kähler structures on specific nilpotent Lie groups without symplectic forms, expanding understanding of their geometric features.

Findings

Identification of semi-Kähler structures on certain nilpotent Lie groups

Analysis of geometric properties of these structures

Extension of known structures to non-symplectic cases

Abstract

It is known that there are 34 classes of six-dimensional nilpotent Lie groups, many of which admit left-invariant symplectic and complex structures. Among them there are three classes of groups on which there are no left-invariant symplectic structures, but there are complex structures. In this work, semi-K\"{a}hler and almost para-semi-K\"{a}hler structures are defined on such Lie groups and their geometric properties are studied.