  A new approach for investigating the classical dynamics of the relativistic
string model with rigidity is proposed. It is based on the embedding of the
string world surface into the space of a constant curvature. It is shown that
the rigid string in flat space-time is described by the Euler-Lagrange equation
for the Willmore functional in a space-time of the constant curvature K=-g/(2
a), where g and a are constants in front of the Nambu-Goto term and the
curvature term in the rigid string action respectively. For simplicity the
Euclidean version of the rigid string in the three-dimensional space-time is
considered. The Willmore functional (the action for the "Willmore string") is
obtained by dropping the Nambu-Goto term in the Polyakov-Kleinert action for
the rigid string. Such "reduction" of the rigid string model would be useful,
for example, by applying some results about the Numbu-Goto string dynamics in
the de Sitter universe to the rigid string model in the Minkowski space-time.
It allows also to use numerous mathematical results about the Willmore surfaces
in the context of the physical problem.
