Φ_(S,F)-调和映射的稳定性  

Stability ofΦ_(S,F)-harmonic Map

作　　者：韩英波 薛玉莹 王艳 韩晓园 HAN Yingbo;XUE Yuying;WANG Yan;HAN Xiaoyuan(College of Mathematics and Statistics,Xinyang Normal University,Xinyang 464000,China)

机构地区：[1]信阳师范学院数学与统计学院,河南信阳464000

出　　处：《信阳师范学院学报（自然科学版）》2022年第2期173-179,共7页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11971415);信阳师范学院“南湖学者奖励计划”青年项目;信阳师范学院研究生科研创新基金项目(2020KYJJ03,2021KYJJ46)。

摘　　要：引入与黎曼流形间的光滑映射有关的能量泛函Φ_(S,F),得到泛函Φ_(S,F)的第一变分公式和第二变分公式,利用第二变分公式,研究Φ_(S,F)-调和映射的稳定性,进而得到从球面S^(m)(m≥5)出发的或到达球面S^(n)(n≥5)的Φ_(S,F)-调和映射的稳定性结果。A generalized functionalΦ_(S,F)associated to maps between Riemannian manifolds is mainly studied.The first variation formula and the second variation formula ofΦ_(S,F)are derived.By using the second variation formula,the stability ofΦ_(S,F)-harmonic map is studied and the stability results ofΦ_(S,F)-harmonic maps from sphere S^(m)(m≥5)or into sphere S^(n)(n≥5)are obtained.

关 键 词：Φ_(S F)-调和映射 稳定性 应力-能量张量 变分公式 

分 类 号：O186.1[理学—数学]