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arXiv · 1204.5915

Exemples de sous variétés de $\mathbb{S}^n$; les variétés proprement biharmoniques avec indice et les variétés proprement C--harmoniques

Vincent Bérard
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Abstract

We call indexed-biharmonic maps, the solutions of a particular non linear elliptic PDE of order 4. This is a generalization of harmonic maps which verifies that biharmonic maps are biharmonic of index 0. The goal of this article is to study submanifolds of $\mathbb{S}^n$ whose inclusion is non harmonic and indexed-biharmonic (i.e. proper indexed-biharmonic). We give some pseudo-umbilical and non pseudo-umbilical examples and we study the link between the proper indexed-biharmonic submanifolds of $\mathbb{S}^n$ and the proper conformal-harmonic submanifolds of $\mathbb{S}^n$.

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Vincent Bérard. 2012-04-26. Exemples de sous variétés de $\mathbb{S}^n$; les variétés proprement biharmoniques avec indice et les variétés proprement C--harmoniques. https://arxiv.org/abs/1204.5915

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