  For a Kahler metric, the Riemannian scalar curvature is equal to twice the
Chern scalar curvature. The question we address here is whether this
equivalence can hold for a non-Kahler Hermitian metric. For such metrics, if
they exist, the Chern scalar curvature would have the same geometric meaning as
the Riemannian scalar curvature. Recently, Liu-Yang showed that if this
equivalence of scalar curvatures holds even in average over a compact Hermitian
manifold, then the metric must in fact be Kahler. However, we prove that a
certain class of noncompact complex manifolds do admit Hermitian metrics for
which this equivalence holds. Subsequently, the question of to what extent the
behavior of said metrics can be dictated is addressed and a classification
theorem is proved.
