@article {2006,
	title = {On geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on distributions of corank 1},
	journal = {J. Math. Sci. 135 (2006) 3168-3194},
	number = {arXiv.org;math/0406111v1},
	year = {2006},
	abstract = {The present paper is devoted to the problem of (local) geodesic equivalence of Riemannian metrics and sub-Riemannian metrics on generic corank 1 distributions. Using Pontryagin Maximum Principle, we treat Riemannian and sub-Riemannian cases in an unified way and obtain some algebraic necessary conditions for the geodesic equivalence of (sub-)Riemannian metrics. In this way first we obtain a new elementary proof of classical Levi-Civita\\\'s Theorem about the classification of all Riemannian geodesically equivalent metrics in a neighborhood of so-called regular (stable) point w.r.t. these metrics. Secondly we prove that sub-Riemannian metrics on contact distributions are geodesically equivalent iff they are constantly proportional. Then we describe all geodesically equivalent sub-Riemannian metrics on quasi-contact distributions. Finally we make the classification of all pairs of geodesically equivalent Riemannian metrics on a surface, which proportional in an isolated point. This is the simplest case, which was not covered by Levi-Civita\\\'s Theorem.},
	doi = {10.1007/s10958-006-0151-5},
	url = {http://hdl.handle.net/1963/2205},
	author = {Igor Zelenko}
}
