In this paper we present a steepest descent method with Armijo's rule for
multicriteria optimization in the Riemannian context. The well definedness of
the sequence generated by the method is guaranteed. Under mild assumptions on
the multicriteria function, we prove that each accumulation point (if they
exist) satisfies first-order necessary conditions for Pareto optimality.
Moreover, assuming quasi-convexity of the multicriteria function and
non-negative curvature of the Riemannian manifold, we prove full convergence of
the sequence to a Pareto critical.