Grassmann流形上Pontrjagin示性式的积分式公式

The Integral Formnla of Pontrjagin Characteristic Formon a Grassmann Manifold

中文关键词:  Grassmann流形  Schubert流形  Pontrjagin示性式

英文关键词:Grassmann manifold  Schubert variety  Pontrjagin characteristic form

中文摘要:

      命Ｇ_n+m,n是一个Ｇｒａｓｓｍａｎｎ流形，Ｚ_2k＝是Ｇ_n+m,n的一个Ｓｃｈｕｂｅｒｔ流形。命Ｅ是Ｇ_n+m,n上的规范矢丛，ＥＣ是Ｅ的变化，Ｅ是ＥＣ的相配酉（ｎ－２ｋ）－标架丛，并且Ｅ′是ＥＣ的一个矢丛，本文证明了下列积分公式：其中ｃ_4k是Ｇ_n+m,n的４ｋ链，Ｐ_k（Ω）是Ｇ_n+m,n的第ｋ个Ｐｏｎｔｒｊａｇｉｎ示性式，是定义在Ｅ和Ｅ′上的（４ｋ－１）－形式。

英文摘要:

      Let G_n+m,n=be a Grassmann manifold. Z_2k is a Schubert variety of G_n+m,n. Let E be the canonicalvector bundle on G_n+m,n and E C is the complexification of E. Let E be the associ-ated unitary in (n-2k)-frame bundle of E C, and E′ is a subbundle of E C.In thispaper, we prove the following integral formula:where C_4k is a 4k-dimensional chain of G_n+m,n, and P_k(Ω)is the kth Pontrjagin charac-teristic form of G_n+m,n T and T′are the (4k-1)-forms defined on E and E′respectively.