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

页码：733 / 742

页数：10

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