An invariant cone in the space of curvature operators is one that is preserved by a flow. For Ricci flow, the condition R ≥ 0 is preserved in all dimensions, while the conditionR ≤ 0 is preserved only in real dimension two. Positive curvature operator is preserved in all dimensions [11], but positive sectional curvature is not preserved in dimensions four and above. The known counterexamples, c...