  On a Hermitian manifold, the Chern connection can induce a metric connection
on the background Riemannian manifold. We call the sectional curvature of the
metric connection induced by the Chern connection the Chern sectional curvature
of this Hermitian manifold. First, we derive expression of the Chern sectional
curvature in local complex coordinates. As an application, we find that a
Hermitian metric is K\"ahler if the Riemann sectional curvature and the Chern
sectional curvature coincide. As subsequent results, Ricci curvature and scalar
curvature of the metric connection induced by the Chern connection are
obtained.
