On the generalization of biharmonic hypersurfaces and biharmonic curves

TL;DR

This paper generalizes the concepts of biharmonic hypersurfaces and curves to include $(p,q)$-harmonic cases in Riemannian manifolds, providing new examples and broadening the understanding of their geometric properties.

Contribution

It introduces a broader framework for $(p,q)$-harmonic hypersurfaces and curves, including explicit examples in space forms, extending previous biharmonic theories.

Findings

New explicit examples of proper $(p,q)$-harmonic hypersurfaces.

Extension of biharmonic concepts to $(p,q)$-harmonic cases.

Broader characterization in Riemannian and Einstein spaces.

Abstract

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.