On p-biharmonic submanifolds in nonpositively curved manifolds

Abstract

Let u: (M, g) → (N, h) be a map between Riemannian manifolds (M, g) and (N, h). The p-bienergy of u is τ_p(u) = ∫_M|τ(u)|^p dν_g, where τ(u) is the tension field of u and p > 1. Critical points of τ_p are called p-biharmonic maps and isometric p-biharmonic maps are called p-biharmonic submanifolds. When p = 2, p-biharmonic submanifolds are biharmonic submanifolds and in recent years many nonexistence results are found for biharmonic submanifolds in nonpositively curved manifolds. In this paper we will study the nonexistence result for general p-biharmonic submanifolds.