  We compute curvatures of a family of tractable metrics on Stiefel manifolds,
introduced recently by H{\"u}per, Markina and Silva Leite, which includes the
well-known embedded and canonical metrics on Stiefel manifolds as special
cases. The metrics could be identified with the Cheeger deformation metrics. We
identify parameter values in the family to make a Stiefel manifold an Einstein
manifold and show Stiefel manifolds always carry an Einstein metric. We analyze
the sectional curvature range and identify the parameter range where the
manifold has non-negative sectional curvature. We provide the exact sectional
curvature range when the number of columns in a Stiefel matrix is $2$, and a
conjectural range for other cases. We derive the formulas from two approaches,
one from a global curvature formula derived in our recent work, another using
curvature formulas for left-invariant metrics. The second approach leads to
curvature formulas for Cheeger deformation metrics on normal homogeneous
spaces.
