Vanishing Theorem for Irreducible Symmetric Spaces of Noncompact Type  

作　　者：Xu Sheng LIU 

机构地区：[1]School of Mathematical Sciences, Fudan University, Shanghai 200433, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2010年第2期361-368,共8页数学学报（英文版）

摘　　要：We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and M ≠SO0（2, 2）/SO（2） × SO（2）. Let π ： E →＊ M be any vector bundle. Then any E-valued L2 harmonic 1-form over M vanishes. In particular we get the vanishing theorem for harmonic maps from irreducible symmetric spaces of noncompact type.We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and M ≠SO0（2, 2）/SO（2） × SO（2）. Let π ： E →＊ M be any vector bundle. Then any E-valued L2 harmonic 1-form over M vanishes. In particular we get the vanishing theorem for harmonic maps from irreducible symmetric spaces of noncompact type.

关 键 词：vanishing theorem symmetric space harmonic form 

分 类 号：O174.41[理学—数学] O186.16[理学—基础数学]