Biharmonic Immersion in Cartan Hadamard manifold

Abstract

If $(N^{m+p},h)$ is a Cartan-Hadamard manifold such that $Ric(h)\ge -G(r_N(x))$ where $G(0)\ge 1,G^{{}^{\prime }}\ge 0$ and $G^{-1/2}\notin L^1(+\infty )$ then every proper biharmonic isometric immersion $\varphi :M^m\to (N^{m+p},h)$ is a harmonic map.

in French

References in corpus (1)

• Biminimal properly immersed submanifolds in complete Riemannian manifolds of non-positive curvature