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arXiv · 1611.03634

Left-invariant Sub-Riemannian Engel structures: abnormal geodesics and integrability

Ivan Beschastnyi·Alexandr Medvedev
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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.

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Ivan Beschastnyi, Alexandr Medvedev. 2016-11-11. Left-invariant Sub-Riemannian Engel structures: abnormal geodesics and integrability. https://arxiv.org/abs/1611.03634

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