Boundedness of scalar curvature gives boundedness of sectional curvature?

Question

Let $(X,\omega)$ be a compact Kahler manifold which the scalar curvature is bounded then the sectional curvature is bounded?

Answer 1

On a compact manifold $M$ with metric of class $C^{2}$, the sectional curvature is bounded without qualification, since the sectional curvature may be viewed as a continuous, real-valued function on the bundle of oriented $2$-planes in the tangent bundle $TM$, and this Grassmann bundle is compact if $M$ is compact.