# Classifying solutions to Romans supergravity with a zero B-field

## TL;DR

This paper classifies geometric solutions in six-dimensional Romans supergravity with a non-trivial R-symmetry gauge field, focusing on cases where the B-field is turned off, revealing a fibration structure over a Kähler base.

## Contribution

It provides a classification of solutions in Romans supergravity with a zero B-field, extending previous work with new geometric insights.

## Key findings

- Six-dimensional space is a two-dimensional fibration over a four-dimensional Kähler manifold.
- Derived differential constraints on an SU(2) structure for solution classification.
- Identified specific geometric structures corresponding to solutions.

## Abstract

Expanding on previous papers, we continue studying Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. Using a set of differential constraints on a $SU(2)$ structure, we look for further geometric solutions to such equations when we turn off the two-form potential B. We find that the six-dimensional space is described by a two-dimensional fibration over a four-dimensional manifold with a K\"ahler metric. We then classify these types of solutions.