Then we offer an intrinsic theoretical framework to reveal the inner relationships among three theories for Eu-ler characteristic number including Gauss-Bonnet-Chern theorem, Hopf-Poincare theorem and Morse theory.

• 利用这一结果,本文揭示了描述欧拉示性数三种不同的理论的内在联系,即Gauss-Bonnet-Chern定理,Hopf-Poincare定理和Morse理论三者之间的内蕴关系。