Some constructions of biharmonic maps and Chen's conjecture on biharmonic hypersurfaces
Some constructions of biharmonic maps and Chen's conjecture on biharmonic hypersurfaces
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DOI：
10.1016/j.geomphys.2011.12.014
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发表时间：
2009-12
期刊：
影响因子：
--
通讯作者：
Ye-lin Ou
中科院分区：
文献类型：
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作者：
Ye-lin Ou
我们给出了几种构造方法，并使用它们生成许多适当双调和映射的示例，包括欧几里得球体中任何维度的双调和环面（定理 2.2、推论 2.3、2.4 和 2.6）、球体之间的双调和映射（定理 2.9）以及通过正交乘法和特征图生成球体（定理 2.10）的双调和映射。我们还研究了映射的双调和图，推导了其图为欧几里得空间中的双调和超曲面的函数方程，并利用双调和图方程（定理4.1）给出了陈氏双调和超曲面猜想的等价表述，为该猜想的解析研究铺平了道路。
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, Corollaries 2.3, 2.4 and 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.