摘要
为了给出Aliyah-Singer定理的分析证明,Gilbey发表了他的定理[1],后来Aliyah-Bott-Patodi等人把他的证明加以简化[2],本文则对Aliyah等人的证明进一步简化,并对流形是定向的情形作了补充。
In order to give an analytic proof of the Atiyah-Siger Index Theorem,Gilkey published his Theorrem, then Atiyah-Bott-Patodi gave another simplified proof.In this paper, we give a more simplified proof and a generalization of manifold to the orientable case.
关键词
黎曼流形
椭圆算子
Gilkey定理
Riemannian manifold, elliptic operator, Atiyah-Singer index theorem, Gilkey theorem
