The extremum of the Willmore-like functional for m-dimensional Riemannian m
anifold immersed in d-dimensional Riemannian manifold under normal variatio
ns is studied and various cases of interest are examined. This study is use
d to relate the parameters of QCD string action, including the Polyakov-Kle
inert extrinsic curvature action, with the geometric properties of the worl
d sheet. The world sheet has been shown to have negative stiffness on the b
asis of the geometric considerations. (C) 2001 Elsevier Science B.V. All ri
ghts reserved.