GENERAL DECOMPOSITION OF SPIN CONNECTION AND TOPOLOGICAL-STRUCTURE INGAUSS-BONNET-CHERN DENSITY

By means of devices of geometric algebra the general decomposition of spin connection on the sphere bundle of a compact n-dimensional Rieman nian manifold has been studied in detail. Using this decomposition the ory it is shown that the Gauss-Bonnet-Chern density of the Euler-Poinc are characteristic can be expressed in terms of a smooth vector field phi and take the form of the delta function delta(phi). The topologica l structure in Gauss-Bonnet-Chern theorem is reviewed.