On the generalized of $p$-biharmonic and bi-$p$-harmonic maps

TL;DR

This paper extends the definitions of $p$-biharmonic and bi-$p$-harmonic maps between Riemannian manifolds and investigates their properties, broadening the theoretical understanding of these generalized harmonic maps.

Contribution

It introduces generalized definitions of $p$-biharmonic and bi-$p$-harmonic maps and explores their fundamental properties, filling a gap in the theoretical framework.

Findings

Extended the definition of $p$-biharmonic maps.

Extended the definition of bi-$p$-harmonic maps.

Analyzed properties of the generalized maps.

Abstract

In this note, we extend the definition of $p$-biharmonic and bi-$p$-harmonic maps between two Riemannian manifolds and explore some of their properties.