  In this paper we prove that if the geodesic flow of a {compact or
non-compact} complete manifold without conjugate points is of the Anosov type,
then the average of the integral of the sectional curvature along the geodesic
is negative and away from zero from a uniform time. Moreover, in dimension two,
if the manifold has no focal points, then this condition is sufficient to
obtain that the geodesic flow is of Anosov type. This sufficient condition will
also be used to construct new examples of non-compact surfaces whose geodesic
flow is of the Anosov type.
