Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606157 | Differential Geometry and its Applications | 2013 | 16 Pages |
Abstract
Let x:M→Emx:M→Em be an isometric immersion from a Riemannian n-manifold into a Euclidean m -space. Denote by Δ and x→ the Laplace operator and the position vector of M, respectively. Then M is called biharmonic if Δ2x→=0. The following Chenʼs Biharmonic Conjecture made in 1991 is well-known and stays open: The only biharmonic submanifolds of Euclidean spaces are the minimal ones . In this paper we prove that the biharmonic conjecture is true for δ(2)δ(2)-ideal and δ(3)δ(3)-ideal hypersurfaces of a Euclidean space of arbitrary dimension.
Keywords
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Bang-Yen Chen, Marian Ioan Munteanu,