论文标题
稳定性和riemannian歧管中Biharmonic Hyperfaces的指数
Stability and the index of biharmonic hypersurfaces in a Riemannian manifold
论文作者
论文摘要
在本文中，我们为riamannian歧管中的双旋次超表面提供了明显的第二变化公式，类似于最小的超浮雕。然后，我们使用第二个变体公式来计算欧几里得球中已知的双旋转性高空曲面的稳定性指数，并证明在欧几里得空间或超薄空间中不稳定适当的Biharmonic Hypersurface的不稳定性，这增加了另一个特殊情况，这增加了Chen猜想Chen的构想对Biharmornom sipmanifolds的构想。
In this paper, we give an explicit second variation formula for a biharmonic hypersurface in a Riamannian manifold similar to that of a minimal hypersurface. We then use the second variation formula to compute the stability index of the known biharmonic hypersurfaces in a Euclidean sphere, and to prove the non-existence 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.
