  Motivated by research on contraction analysis and incremental
stability/stabilizability the study of 'differential properties' has attracted
increasing attention lately. Previously lifts of functions and vector fields to
the tangent bundle of the state space manifold have been employed for a
geometric approach to differential passivity and dissipativity. In the same
vein, the present paper aims at a geometric underpinning and elucidation of
recent work on 'control contraction metrics' and 'generalized differential
Riccati equations'.
