Abstract
We shall consider a Hermitian n-vector bundle E over a complex manifold X. When X is compact (without boundary), S.S. Chern defined in his paper [3] the Chern classes (the basic characteristic classes of E) Ĉi(E), i = 1, · · ·, n, in terms of the basic forms Φi on the Grassmann manifold H(n, N) and the classifying map f of X into H(n, N). Moreover he proved ([3], [4]) that if Ek denotes the k-general Stiefel bundle associated with E, the (n — k + 1)-th Chern class Ĉn-k+1(E) coincides with the characteristic class C(Ek) of Ek defined as follows: Let K be a simplicial decomposition of X and K2(n-k)+1 the 2(n — k) + 1 — shelton of K.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
