Geometric properties of QCD string from Willmore functional

The extremum of the Willmore-like functional for m-dimensional Riemannian manifold immersed in d-dimensional Riemannian manifold under normal variations is studied and various cases of interest are examined. This study is used to relate the parameters of QCD string action, including the Polyakov-Kleinert extrinsic curvature action, with the geometric properties of the world sheet. The world sheet has been shown to have negative stiffness on the basis of the geometric considerations.