Quadratic sufficient conditions for the minimality for abnormal sub-Riemannian geodesics (Q2777854)

This paper investigates quadratic order sufficient conditions for minimality of abnormal trajectories in the problem of shortest paths in sub-metrics, in particular, it can be sub-Riemannian metrics. Here sub-metrics are arbitrary positive sub-linear functionals. The author obtains the final form of quadratic order sufficient conditions of minimality. These conditions coincide with quadratic order sufficient conditions of rigidity. On the other hand the following result is proved. NEWLINENEWLINENEWLINEIf a trajectory is quadratically rigid, then in any strong convex sub-metric it gives the strong minimum of the distance between two given points, but it may becomes non-singular. Also the case of Pontryagin's minimum and Pontryagin's rigidity are considered.NEWLINENEWLINEFor the entire collection see [Zbl 0949.00043].