【作者】 贾高杨；

【导师】 周振荣；

【作者基本信息】 华中师范大学 ， 基础数学， 2011， 硕士

【摘要】 用F(‖R▽‖2/2)替换Yang-Mills泛函的积分,我们得到了F-Yang-Mills泛函,进而得到F-Yang-Mills场,这里的F是一个非负且C∞的函数。本文计算了F-Yang-Mills场的第一和第二变分,并研究了欧氏空间和球面的子流形上的F-Yang-Mills场的间隙性和不稳定性质。在文章的最后,我们研究了F-Yang-Mills场得特殊例子——指数-Yang-Mills场。更多还原

【Abstract】 Replacing the integrand of the Yang-Mills functional by F(‖R▽‖2/2) define an F-Yang-mills functional,and hence F-Yang-Mills fields,where F is a non-negative and C∞function.The first and second variations are calculated,the gaps and instabilities of F-Yang-Mills fields on some submanifolds of the Euclidean spaces and the spheres are investigated.In the last, we studied exp-Yang-Mills fields,which is a special case of F-Yang-Mills fields.更多还原