  We obtain a Landau -- Hadamard type inequality for mappings defined on the
whole real axis and taking values in Riemannian manifolds. In terms of an
auxiliary convex function, we find conditions under which the boundedness of
covariant derivative along the curve under consideration ensures the
boundedness of the corresponding tangent vector field. As an example we obtain
a Landau -- Hadamard type inequality for curves on 2D unite sphere.
