de Rham-Hodge-Signature算子的局部指标定理

吴发恩

数学学报 ›› 1996, Vol. 39 ›› Issue (6)

PDF(466 KB)
PDF(466 KB)
数学学报 ›› 1996, Vol. 39 ›› Issue (6) DOI: 10.12386/A1996sxxb0113
论文

de Rham-Hodge-Signature算子的局部指标定理

    吴发恩
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Local Index Theorem for de RHam-Hodge-Signature Operator

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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.

Abstract

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.

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MP拟基本解 / 热核 / 局部指标 / 超迹 / deRham-Hodgde-Signature算子

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吴发恩. de Rham-Hodge-Signature算子的局部指标定理. 数学学报, 1996, 39(6) https://doi.org/10.12386/A1996sxxb0113
Local Index Theorem for de RHam-Hodge-Signature Operator. Acta Mathematica Sinica, Chinese Series, 1996, 39(6) https://doi.org/10.12386/A1996sxxb0113
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