A generalization of the isoperimetric inequality on $S\sp 2$ and flat tori in $S\sp 3$

A geometric inequality is proved for closed curves on ${S^2}$ which are regularly homotopic to simple closed curves. This generalizes the classical isoperimetric inequality for simple closed curves on ${S^2}$. The proof is based on the study of flat tori in ${S^3}$ and their images under the Gauss map.