【摘要】 设M是球面Sn+p中的n维紧致定向的浸入子流形,则存在一个仅与M的第二基本形式长度平方和平均曲率有关的正常数A,当n>4+A时,M上不存在非平凡的弱稳定的Yang-Mills场。从而推广了Simons的关于球面Sn是Yang-Mills不稳定的经典定理。本文也证明了球面的紧致子流形上的Yang-Mills场,存在空隙性现象。更多还原

【Abstract】 If M is an n-dimensional compact oriented submanifold immersed in a sphere Sn+p, it is proved that, if n > 4 + A + 2σ where σ is the square length of the second fundamental form and A is a positive constant depending only on the square length of the second fundamental form and the mean curvature of M, there are no non-trivial weakly stable Yang-Mills fields on M. Thus we generalize a classical result due to Simons that the standard sphere Sn(n > 4) is Yang-Mills unstable. It is also shown that there is a gap phenomena for Yang-Mills fields on the compact submanifolds in the sphere.更多还原