|XXXV Workshop on Geometric Methods in Physics
Local optimality of sub-Riemannian geodesics
It is well-known that normal extremals in sub-Riemannian geometry are curves which locally minimize the energy functional. However, the known proofs of this fact are computational and the relation of the local optimality with the geometry of the problem remains unclear. In the talk I will provide a new proof of this result, which gives insight into the geometric reasons of local optimality. Also the the relation of the regularity of normal extremals with their optimality become apparent in our approach.The talk is based on a joint work with professor Witold Respondek.