Closed Biconservative Hypersurfaces in Spheres

We characterise the profile curves of non-CMC biconservative rotational hypersurfaces of space forms $N^n(\rho )$ as $p$-elastic curves, for a suitable rational number $p\in [1\mathrm{/}4,1)$ which depends on the dimension $n$ of the ambient space. Analysing the closure conditions of these $p$-elastic curves, we prove the existence of a discrete biparametric family of non-CMC closed (i.e., compact without boundary) biconservative hypersurfaces in ${\mathbb{S}}^n(\rho )$. None of these hypersurfaces can be embedded in ${\mathbb{S}}^n(\rho )$.