  The aim of this paper is to present an extragradient method for variational
inequality associated to a point-to-set vector field in Hadamard manifolds and
to study its convergence properties. In order to present our method the concept
of $\epsilon$-enlargement of maximal monotone vector fields is used and its
lower-semicontinuity is stablished in order to obtain the convergence of the
method in this new context.
