  Motivated from the action functional for bosonic strings with extrinsic
curvature term we introduce an action functional for maps between Riemannian
manifolds that interpolates between the actions for harmonic and biharmonic
maps. Critical points of this functional will be called interpolating
sesqui-harmonic maps. In this article we initiate a rigorous mathematical
treatment of this functional and study various basic aspects of its critical
points.
