Real analytic $\mathrm{S}\mathrm{L}(n,\mathbb{R})$-actions on closed manifolds

We classify real-analytic $\mathrm{S}\mathrm{L}(n,\mathbb{R})$-actions on closed manifolds of dimension m for $3\le n\le m\le 2n-3$, which extends Fisher–Melnick’s work for $\mathrm{S}\mathrm{L}(n,\mathbb{R})$-actions on closed n-manifolds. Additionally, we classify smooth $\mathrm{S}\mathrm{L}(n,\mathbb{R})$-actions on closed m-manifolds that are fixed-point free. As a corollary, we obtain the density or non-density of structural stability of fixed-point free $\mathrm{S}\mathrm{L}(n,\mathbb{R})$-actions.