Left invariant nearly pseudo-K\"{a}hler structures and the tangent lie group

TL;DR

This paper demonstrates that if a Lie group has a left invariant nearly pseudo-K"{a}hler structure, then its tangent bundle naturally inherits a similar structure, linking geometric properties of the group to its tangent bundle.

Contribution

It establishes that the tangent bundle of a Lie group with a left invariant nearly pseudo-K"{a}hler structure also admits such a structure, extending the geometric framework.

Findings

Tangent bundle inherits nearly pseudo-K"{a}hler structure

Left invariance is preserved in the tangent bundle

Provides a method to construct new nearly pseudo-K"{a}hler structures

Abstract

Let $G$ be a Lie group, and let $(g,J)$ be a left invariant almost pseudo-Hermitian structure on $G$. It is shown that if $(g,J)$ is also nearly pseudo-K\"{a}hler, then the tangent bundle $TG$ (with its natural Lie group structure induced from $G$) admits a left-invariant nearly pseudo-K\"{a}hler structure.