Left-invariant Sub-Riemannian Engel structures: abnormal geodesics and integrability
Differential Geometry
2018-05-03 v2 Optimization and Control
Abstract
We provide the first known family of examples of integrable homogeneous sub-Riemannian structures admitting strictly abnormal geodesics. These examples were obtained through the analysis of the equivalence problem for sub-Riemannian Engel structures. We formulate a criterion of strict abnormality in terms of structure functions of a canonical frame on a sub-Riemannian Engel manifold as well as estimates on conjugate times.
Cite
@article{arxiv.1611.03634,
title = {Left-invariant Sub-Riemannian Engel structures: abnormal geodesics and integrability},
author = {Ivan Beschastnyi and Alexandr Medvedev},
journal= {arXiv preprint arXiv:1611.03634},
year = {2018}
}
Comments
For more clarity we have considerably reworked and shortened this text