$C^2$-robust heterodimensional tangencies

In this paper, we give sufficient conditions for the existence of $C^2$ robust heterodimensional tangency, and present a nonempty open set in ${\text{Diff}}^2(M)$ with $\dim (M)\ge 3$ each element of which has a non-degenerate heterodimensional tangency on a $C^2$ robust heterodimensional cycle.