  Intrinsic and extrinsic geometric properties of string world sheets in curved
space-time background are explored. In our formulation, the only dynamical
degrees of freedom of the string are its immersion coordinates. Classical
equation of motion and the space-time energy-momentum tensor of the string are
obtained. The equations of motion for the extrinsic curvature action are second
order for the scalar mean curvature of the world sheet. 1-loop divergent terms
are calculated using the background field method. Asymptotic freedom of the
extrinsic curvature coupling is established.
