Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1893768 | Journal of Geometry and Physics | 2012 | 12 Pages |
Abstract
We give several construction methods and use them to produce many examples of proper biharmonic maps including biharmonic tori of any dimension in Euclidean spheres (Theorem 2.2, Corollary 2.3, Corollary 2.4 and Corollary 2.6), biharmonic maps between spheres (Theorem 2.9) and into spheres (Theorem 2.10) via orthogonal multiplications and eigenmaps. We also study biharmonic graphs of maps, derive the equation for a function whose graph is a biharmonic hypersurface in a Euclidean space, and give an equivalent formulation of Chen’s conjecture on biharmonic hypersurfaces by using the biharmonic graph equation (Theorem 4.1) which paves a way for the analytic study of the conjecture.
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Ye-Lin Ou,