On the generalization of biharmonic hypersurfaces and biharmonic curves

In this work, we extend the concepts of $p$-biharmonic maps and $p$-biharmonic hypersurfaces to provide a broader characterization of $(p,q)$-harmonic hypersurfaces and $(p,q)$-harmonic curves in Riemannian manifolds, including Einstein spaces. Moreover, we present new explicit examples of proper $(p,q)$-harmonic hypersurfaces and $(p,q)$-harmonic curves in space forms.