多重调和映照的广义Frenet公式及其应用  

Generalized Frenet formulae for pluriharmonic.

作　　者：吴炳烨[1] 

机构地区：[1]浙江大学数学系

出　　处：《浙江大学学报（理学版）》2002年第4期369-372,共4页Journal of Zhejiang University（Science Edition）

基　　金：浙江省重点学科基金资助项目 .

摘　　要：采用活动标架法研究复流形到复 Grassmann流形的多重调和映照的性质 .建立了广义 Frenet公式 ,应用它研究了多重调和映照的若干性质 .利用 Maurer- Cartan形式的拉回得到了多重调和映照为强共形的必要条件 ,它在一定条件下也是充分的 .利用多重调和映照的 Gauss丛的多重调和性给出了判断迷向阶的一个方法 。The pluriharmonic maps from complex manifolds into complex Grassmann manifolds by moving frames was studied. The generalized Frenet formulae for pluriharmonic maps are established. As its applications, a necessary condition for pluriharmonic maps to be strongly conformal is obtained by use of pull-back of the Maurer-Cartan forms which is also sufficient under a suitable additional condition. A method is provided to determine the isotropy order of pluriharmonic maps by the pluriharmonicity of the Gauss bundle and thus generalizes the corresponding result for harmonic maps of surfaces into complex projective spaces.

关 键 词：广义Frenet公式 多重调和映照 强共形 迷向阶 活动标贺法 复GRASSMANN流形 

分 类 号：O186.11[理学—数学]