I find an interesting paper that mentioned the Definition of curvature of an affine optimal control system. It reminded me that many textbooks on Riemannian geometry only tell us about metrics, geodesics, parallel transport, and curvature tensors and son on, using some special surfaces with constant curvature as examples. So for a general nonlinear control system (eg. with dissipative force or other external forces), how do we calculate its curvature tensor? Are there more references or research on this topic?

Thank you all for your comments and help!