p-Biharmonic hypersurfaces in Einstein space and conformally flat space

TL;DR

This paper investigates p-biharmonic hypersurfaces within Einstein and conformally flat spaces, offering new properties, characterizations, and examples, and proposing open problems for further research.

Contribution

It introduces new properties and characterizations of p-biharmonic hypersurfaces in specific geometric spaces, including a novel example of proper p-biharmonic hypersurfaces.

Findings

New properties for p-biharmonic hypersurfaces in Riemannian manifolds

Characterization of p-biharmonic submanifolds in Einstein spaces

Construction of a new proper p-biharmonic hypersurface

Abstract

In this paper, we present some new properties for p-biharmonic hypersurfaces in Riemannian manifold. We also characterize the p-biharmonic submanifolds in an Einstein space. We construct a new example of proper p-biharmonic hypersurfaces. We present some open problems.