By making use of the φ-mapping topological current theory,this paper shows that the Gauss-Bonnet-Che densityof δ(φ),which means that only the zeros of φ contribute to X(M).This is the elementary fact of the Hopf theorem.Furthermore,it presents that a new topological tensor current of (~p)-branes can be derived from the Gauss-Bonnet-Chem density.Using this topological current,it obtains the generalized Nambu action for multi (~p)-branes.