Biharmonic Immersion in Cartan Hadamard manifold

Abstract

If $(N^{m+p},h)$ is a Cartan-Hadamard manifold such that $Ric(h)\geq -G(r_{N}(x))$ where $G(0)\geq 1, G^{'}\geq 0$ and $G^{-1/2}\not\in L^{1}(+\infty)$ then every proper biharmonic isometric immersion $\phi : M^{m}\rightarrow(N^{m+p},h)$ is a harmonic map.