  The most usual procedure for deriving curvature corrections to effective
actions for topological defects is subjected to a critical reappraisal. A
logically unjustified step (leading to overdetermination) is identified and
rectified, taking the standard domain wall case as an illustrative example.
Using the appropriately corrected procedure, we obtain a new exact (analytic)
expression for the corresponding effective action contribution of quadratic
order in the wall width, in terms of the intrinsic Ricci scalar $R$ and the
extrinsic curvature scalar $K$. The result is proportional to $cK^2-R$ with the
coefficient given by $c\simeq 2$. The resulting form of the ensuing dynamical
equations is obtained in terms of the second fundamental form and the
Dalembertian of its trace, K. It is argued that this does not invalidate the
physical conclusions obtained from the "zero rigidity" ansatz $c=0$ used in
previous work.
