关于复合微分算子的W-留数

摘要

本文首先综述近年来关于微分算子W-留数的一系列研究进展。之后研究一类复合微分算子D+c(X)的基本结构,并在法坐标系下导出了微分算子的主符号表示,最终结合Lichnerowicz公式给出了5维带边流形上复合微分算子的W-留数表示。In this paper, a series of research advances on W-residue of differential operators in recent years are reviewed. Then the basic structure of a class of complex differential operators D+c(X)is studied, and the principal symbolic representation of differential operators is derived in normal coordinate system. Finally, the W-residue representation of complex differential operators on 5-dimensional manifolds with edges is given by combining Lichnerowicz formula.