Biharmonic PNMC submanifolds in spheres
Biharmonic PNMC submanifolds in spheres
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DOI：
10.1007/s11512-012-0169-5
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发表时间：
2011-10
期刊：
影响因子：
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通讯作者：
A. Balmuş;S. Montaldo;C. Oniciuc
中科院分区：
文献类型：
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作者：
A. Balmuş;S. Montaldo;C. Oniciuc
我们获得了具有平行归一化平均曲率矢量场的双调和子流形的几个刚性结果。我们将双调和子流形分类为平行归一化平均曲率向量场并且最多具有两个不同的主曲率。特别是，我们确定所有具有平行归一化平均曲率向量场的双调和曲面。 然后，我们研究（不一定是紧凑的）真双调和子流形，其类型在 B.-Y 意义上。 陈。我们证明 (i) 1 型或 2 型的真双调和子流形当且仅当它分别具有恒定的平均曲率 f=1 或 f∈(0,1)； (ii) 不存在具有平行归一化平均曲率向量场的真双调和 3 型子流形。
We obtain several rigidity results for biharmonic submanifolds inwith parallel normalized mean curvature vector fields. We classify biharmonic submanifolds inwith parallel normalized mean curvature vector fields and with at most two distinct principal curvatures. In particular, we determine all biharmonic surfaces with parallel normalized mean curvature vector fields in.Then we investigate, for (not necessarily compact) proper-biharmonic submanifolds in, their type in the sense of B.-Y. Chen. We prove that (i) a proper-biharmonic submanifold inis of 1-type or 2-type if and only if it has constant mean curvaturef=1 orf∈(0,1), respectively; and (ii) there are no proper-biharmonic 3-type submanifolds with parallel normalized mean curvature vector fields in.