Locally conformally K\"ahler structures on four-dimensional solvable Lie algebras

TL;DR

This paper classifies locally conformally K"ahler structures on four-dimensional solvable Lie algebras, providing new examples and geometric insights, with implications for higher-dimensional manifolds such as Oeljeklaus-Toma manifolds.

Contribution

It offers a comprehensive classification of lcK structures on 4D solvable Lie algebras and connects these to higher-dimensional geometric structures.

Findings

Many new lcK examples on higher-dimensional manifolds

Geometric interpretation of 4D lcK structures

Classification up to linear equivalence

Abstract

We classify and investigate locally conformally K\"ahler structures on four-dimensional solvable Lie algebras up to linear equivalence. As an application we can produce many examples in higher dimension, here including lcK structures on Oeljeklaus-Toma manifolds, and we also give a geometric interpretation of some of the $4$-dimensional structures in our classification.