Rigidity properties of p-biharmonic maps and p-biharmonic submanifolds

Abstract

We give some rigidity properties of a p-biharmonic map u:(M,g)→(N,h) between Riemannian manifolds (Mn,g) and (Nm,h). We first provide various sufficient conditions for p-biharmonic maps to be harmonic. Moreover, when the map u is an isometric immersion, by assuming that the Ln2-norm of the sectional curvature on M is sufficiently small or if the fundamental tone of the p-biharmonic submanifold is sufficiently big, it is proved that M is minimal.