  The extremum of the Willmore-like functional for $m$-dimensional Riemannian
surface 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 {\it{negative stiffness}} on the basis
of geometric considerations.
