Geometric properties of QCD string from Willmore functional

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.