Geometry of Biharmonic Submanifolds

Abstract

Harmonic maps are mappings between Riemannian manifolds which extremize a natural energy functional. They include geodesics, minimal surfaces. p-harmonic maps with (p 2) de ned as critical points of the p-energy functional. The p-biharmonic maps are generalization of the notion of p-harmonic. In this work, we study p-biharmonic submanifolds. The main result are • The de nition of p-biharmonic submanifold; • The necessary conditions for submanifold to be p-biharmonic submanifold in space form; • Some properties for p-biharmonic hypersurfaces in Riemannian submanifolds in an Einstein space; • the construction of new examples of proper p-biharmonic hypersurfaces.