Closed biconservative hypersurfaces in spheres

Montaldo, S;Oniciuc, C;Pampano, A

2023-01-01

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Abstract

We characterise the profile curves of non-CMC biconservative rotational hyper -surfaces of space forms Nn(rho) as p -elastic curves, for a suitable rational number p & ISIN; [1/4, 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) bicon-servative hypersurfaces in Sn(rho). None of these hypersurfaces can be embedded in Sn(rho).