  We prove the following results: An almost Hermitian manifold of indefinite
metric is of pointwise constant holomorphic sectional curvature if the
holomorphic sectional curvature is bounded from above and from below. If the
antiholomorphic sectional curvature is bounded either from above or from below,
then the manifold is of pointwise constant antiholomorphic sectional curvature.
Similar results are obtained for almost Hermitian manifolds of definite metric.
