Decomposition Theory of Spin Connection and Topological Structure of Gauss-Bonnet-Chern Theorem on Manifold With Boundary
Abstract
Description
The index theorem of Euler-Poincaré characteristic of manifold with boundary is given by making use of the general decomposition theory of spin connection. We shows the sum of the total index of a vector field $ϕ$ and half the total of the projective vector field of $ϕ$ on the boundary equals the Euler-Poincaré characteristic of the manifold. Detailed discussion on the topological structure of the Gauss-Bonnet-Chern theorem on manifold with boundary is given. The Hopf indices and Brouwer degrees label the local structure of the Euler density.
Revtex, 13 pages, no figure
Revtex, 13 pages, no figure