梅向明.Grassmann流形上Pontrjagin示性式的积分式公式[J].数学研究及应用,1995,15(1):1~6
Grassmann流形上Pontrjagin示性式的积分式公式
The Integral Formnla of Pontrjagin Characteristic Formon a Grassmann Manifold
投稿时间:1992-12-26  
DOI:10.3770/j.issn:1000-341X.1995.01.001
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
基金项目:
作者单位
梅向明 首都师范大学数学系 
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中文摘要:
      命Gn+m,n是一个Grassmann流形,Z2k=是Gn+m,n的一个Schubert流形。命E是Gn+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c4k是Gn+m,n的4k链,Pk(Ω)是Gn+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 Gn+m,n=be a Grassmann manifold. Z2k is a Schubert variety of Gn+m,n. Let E be the canonicalvector bundle on Gn+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 C4k is a 4k-dimensional chain of Gn+m,n, and Pk(Ω)is the kth Pontrjagin charac-teristic form of Gn+m,n T and T′are the (4k-1)-forms defined on E and E′respectively.
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