摘要
作者证明了如下结果:设||B||和H分别是单位球面S^(n+2)中n维紧致子流形M的第二基本形式B的模长和平均曲率,且设则当n>4+(?)+2 ||B||~2时,M上不存在非平凡的弱稳定的Yang-M_jlls场。本文也表明了在紧致的共形平坦的黎曼流形上,Yang-Mills场存在空隙性。
We prove the following.Let M be an n-dimensional compact submani-fold with mean cunature H in the sphere Sn+p. Denote ‖B‖ the squarelength of the second fundamental form B.If n>4 + B+ 2‖B‖2there are no non-trivial weakly stable Yang-Mills fields on M, whereThe fact that any weakly stable Yang-Mills fields on the sphere sn(n>4)is trivial can be generalized to the finite product of spheres Sn1x… xSnrfor nt>4,t = 1,…,r or nt>4,ns= l,t = 1,…,r,t≠s( 1≤s≤r). It is also shown that there is the gap phenomena for Yang-Mills fields on the compact conformal flat Riemannian manifolds.
