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math.DG2018
Volume of small balls and sub-Riemannian curvature in 3D contact manifolds
Davide Barilari, Ivan Beschastnyi, Antonio Lerario
We compute the asymptotic expansion of the volume of small sub-Riemannian balls in a contact 3-dimensional manifold, and we express the first meaningful geometric coefficients in t…
math.DG2016
Left-invariant Sub-Riemannian Engel structures: abnormal geodesics and integrability
Ivan Beschastnyi, Alexandr Medvedev
We provide the first known family of examples of integrable homogeneous sub-Riemannian structures admitting strictly abnormal geodesics. These examples were obtained through the an…