  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.
