  We investigate bi-Hamiltonian structures and related mKdV hierarchy of
solitonic equations generated by (semi) Riemannian metrics and curve flow of
non-stretching curves. The corresponding nonholonomic tangent space geometry is
defined by canonically induced nonlinear connections, Sasaki type metrics and
linear connections. One yields couples of generalized sine-Gordon equations
when the corresponding geometric curve flows result in hierarchies on the
tangent bundle described in explicit form by nonholonomic wave map equations
and mKdV analogs of the Schrodinger map equation.
