Biharmonic Immersion in Cartan Hadamard manifold

Saïd Asserda; M'Hamed Kassi

Biharmonic Immersion in Cartan Hadamard manifold

Differential Geometry 2017-07-10 v1

Authors: Saïd Asserda , M'Hamed Kassi

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.

Keywords

Cartan-Hadamard manifold biharmonic immersion harmonic map isometric immersion Ricci curvature differential geometry

Cite

@article{arxiv.1707.01925,
  title  = {Biharmonic Immersion in Cartan Hadamard manifold},
  author = {Saïd Asserda and M'Hamed Kassi},
  journal= {arXiv preprint arXiv:1707.01925},
  year   = {2017}
}

Comments

in French

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