  In this short note, as a simple application of the strong result proved
recently by B\"ohm and Wilking, we give a classification on closed manifolds
with 2-nonnegative curvature operator. Moreover, by the new invariant cone
constructions of B\"ohm and Wilking, we show that any complete Riemannian
manifold (with dimension $\ge 3$) whose curvature operator is bounded and
satisfies the pinching condition $R\ge \delta R_{I}>0$, for some $\delta>0$,
must be compact. This provides an intrinsic analogue of a result of Hamilton on
convex hypersurfaces.
