  In the present article, we study the local features of the world-sheet in the
case when probe bosonic string moves in antisymmetric background field. We
generalize the geometry of surfaces embedded in space-time to the case when the
torsion is present. We define the mean extrinsic curvature for spaces with
Minkowski signature and introduce the concept of mean torsion. Its orthogonal
projection defines the dual mean extrinsic curvature. In this language, the
field equation is just the equality of mean extrinsic curvature and extrinsic
mean torsion, which we call CT-duality. To the world-sheet described by this
relation we will refer as CT-dual surface.
