4TH-ORDER TOPOLOGICAL TENSOR CURRENT AND FOCKS COORDINATE CONDITION

From phi-mapping method we construct a fourth-order topological tensor current in general. It is shown that the inner structure of this topo logical tensor current, is labelled by the delta-function delta(phi), which represents some four-dimensional singular manifolds. By investig ating the total expansion of delta(phi), these singular manifolds carr y the topological numbers beta(i) eta(i) naturally, which does not inv olve any concrete models. As the generalization of Nielsen's Lagrangia n and Nambu's action for strings, we present a new coordinate conditio n in general relativity, which includes the Fock's coordinate conditio n as a special case.