The Integral Formnla of Pontrjagin Characteristic Formon a Grassmann Manifold

Abstract:

      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.