摘要
在空间形式中,均造了子流形的一类泛函,其包含r极小泛函与体积泛函(极小)作为特殊情形,此类泛函的临界点称之为(r+1,λ)-平行子流形.对于(r+1,λ)-平行子流形,给出了代数,微分和变分刻画.更进一步,研究了(r+1,λ)-平行子流形的稳定性,证明了Simons型不存在定理:在一定条件下((r,λ)-函数S_(r,λ)为正),球面中不存在稳定的(r+1,λ)-平行子流形.
A class of functional is found in space forms such that its critical points include r-minimal submanifolds and minimal submanifolds as special cases.The critical points are defined as（→r＋1,→λ）-parallel submanifolds.We obtain algebraic,differential and variational characterizations of the（→r＋1,→λ）-parallel submanifolds.Moreover,we prove a Simons＇ type nonexistence theorem which says that in the unit sphere there exists no stable（→r＋1,→λ）-parallel submanifold with its corresponding（→r→,λ）-function S（→r,→λ） positive.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2013年第5期669-686,共18页
Acta Mathematica Sinica：Chinese Series
