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We give a geometric realization of a subcategory of the $m$-cluster category$\mathcal{C}^m$ of type $\widetilde{A}_{p,q}$, by using $(m+2)$-angulations ofan annulus with $p+q$ marked points. We also give a bijection between anequivalence class of $(m+2)$-angulations and the mutation class of colouredquivers of type $\widetilde{A}_{p,q}$.

A geometric realization of the $m$-cluster category of type $\tilde{A}$