  In this paper, based on the gauge potential decomposition and the
$\phi-$mapping theories, we study the topological structures and properties of
the cosmic strings that arise in the Abelian-Higgs gauge theory in the
zero-thickness limit. After a detailed discussion, we conclude that the
topological tensor current introduced in our model is a better and more basic
starting point than the generally used Nambu-Goto effective action for studying
cosmic strings.
