Ys. Duan et Xg. Lee, GENERAL DECOMPOSITION-THEORY OF SPIN CONNECTIONS TOPOLOGICAL-STRUCTURE OF GAUSS-BONNET-CHERN DENSITY AND THE MORSE-THEORY, Helvetica Physica Acta, 68(6), 1995, pp. 513-530
By means of methods of the geometric algebra the general decomposition
of the spin connections on the sphere bundle of a compact n-dimension
al Riemannian manifold has been studied in detail. Using this decompos
ition theory it is shown that the Gauss-Bonnet-Chern density of the Eu
ler-Poincare characteristic can be expressed as a a-function of a smoo
th vector field delta(<(phi)over right arrow>). The topological struct
ure of the Gauss-Bonnet-Chern density is detailed. Furthermore the Mor
se theory formula of the Euler-Poincare characteristic has been obtain
ed via the topological structure.