Exemples de sous variétés de \mathbbSⁿ; les variétés proprement biharmoniques avec indice et les variétés proprement C--harmoniques

2012/04/26 by Vincent Bérard, Bérard, Vincent
Mathematics · #Advanced Harmonic Analysis Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1204.5915

openalex publication_date 2012/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \mathbbSⁿ 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 \mathbbSⁿ and the proper conformal-harmonic submanifolds of \mathbbSⁿ.

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