  In this paper, we study the generalized Heisenberg ferromagnet equation,
namely, the M-CVI equation. This equation is integrable. The integrable motion
of the space curves induced by the M-CVI equation is presented. Using this
result, the Lakshmanan (geometrical) equivalence between the M-CVI equation and
the two-component Camassa-Holm equation is established. Note that these
equations are gauge equivalent each to other.
