  Within the geometrical framework developed in arXiv:0705.2362, the problem of
minimality for constrained calculus of variations is analysed among the class
of differentiable curves. A fully covariant representation of the second
variation of the action functional, based on a suitable gauge transformation of
the Lagrangian, is explicitly worked out. Both necessary and sufficient
conditions for minimality are proved, and are then reinterpreted in terms of
Jacobi fields.
