Stability and the index of biharmonic hypersurfaces in a Riemannian manifold

被引：3
|
作者：
Ou, Ye-Lin [1 ]
机构：
[1] Texas A&M Univ, Dept Math, Commerce, TX 75429 USA
来源：
ANNALI DI MATEMATICA PURA ED APPLICATA | 2022年 / 201卷 / 02期
关键词：
The second variations of biharmonic hypersurfaces; Stable biharmonic hypersurfaces; The index of biharmonic hypersurfaces; The index of biharmonic torus; Constant mean curvature hypersurfaces; MAPS; SUBMANIFOLDS;
D O I：
10.1007/s10231-021-01135-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we give an explicit second variation formula for a biharmonic hypersurface in a Riemannian manifold similar to that of a minimal hypersurface. We then use the second variation formula to compute the normal stability index of the known biharmonic hypersurfaces in a Euclidean sphere and to prove the nonexistence of unstable proper biharmonic hypersurface in a Euclidean space or a hyperbolic space, which adds another special case to support Chen's conjecture on biharmonic submanifolds.
引用
收藏
页码：733 / 742
页数：10
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