Recently, I find an interesting paper that mentioned the Definition of curvature of an affine optimal control system. It suddenly 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 control system, how do we calculate its curvature tensor? Is this a problem worth studying? Are there any more examples?
Thank you all for your comments and help!