We know that in smooth Riemannian manifolds the exponential map is smooth and in the complete smooth manifolds with nonpositive sectional curvature (Hadamard manifolds) the exponential map is diffeomorphism. Now my question is as follows
When is the exponential map Lipschitz?
More precisely, is it true that in Hadamard manifolds (specially in manifolds with the constant nonpositive sectional curvature) exponential map is Lipschitz?