de　Rham－Hodge－Signature算子的局部指标定理  

Local Index Theorem for de RHam-Hodge-Signature Operator

作　　者：吴发恩[1] 

机构地区：[1]北方交通大学数学系

出　　处：《数学学报（中文版）》1996年第6期833-841,共9页Acta Mathematica Sinica：Chinese Series

摘　　要：整体的Ａｔｉｙａｈ－Ｓｉｎｇｅｒ指标定理对于一般的椭圆微分算子都成立．但对于局部指标定理来说，人们只能对具体的算子给予证明．并且各种情况需个别处理．由［６］知本文中证得的ｄｅＲｈａｍ－Ｈｏｄｇｅ－Ｓｉｇｎａｔｕｒｅ算子的局部指标既不是α型也不是β型的．这和经典的椭圆算子情形不同．There holds the global Atiyah-Singer Index Theorem for general elliptical differential operators. But for local index theorem,people can only give a proof for concrete operator and the teclnique used in the proof varies from one to another.We present here the suitable definition of de Rham-Hodge-Signature operator D and the proof of its locaf index theorem.From[6],we conclude that the local index for D is neither of type α nor type β. This is dtherent from the case of classical elliptic differential operators.

关 键 词：局部指标定理 R-H-S算子 椭圆微分算子 微分几何 

分 类 号：O186.1[理学—数学]