We find the explicit conditions under which a single ordinary differential equation (shortly ODE) of order â‰¥ 4 is (locally) equivalent to the trivial equation under the group of contactâ€¦ (More)

We show that classical Wilczynskiâ€“Se-ashi invariants of linear systems of ordinary differential equations are generalized in a natural way to contact invariants of non-linear ODEs. We exploreâ€¦ (More)

In 1910 E. Cartan constructed the canonical frame and found the most symmetric case for maximally nonholonomic rank 2 distributions in R 5. We solve the analogous problems for rank 2 distributions inâ€¦ (More)

The paper is devoted to the complete classi cation of all real Lie algebras of contact vector elds on the rst jet space of one-dimensional submanifolds in the plane. This completes Sophus Lieâ€™sâ€¦ (More)

Abstract: Some of the well known Fefferman like constructions of parabolic geometries end up with a new structure on the same manifold. In this paper, we classify all such cases with the help of theâ€¦ (More)

We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space W with respect to the action of aâ€¦ (More)

We establish a twistor correspondence between a cuspidal cubic curve in a complex projective plane, and a co-calibrated homogeneous G2 structure on the seven-dimensional parameter space of suchâ€¦ (More)

We study the conditions when locally homogeneous curves in homogeneous spaces admit a natural projective parameter. In particular, we prove that this is always the case for trajectories ofâ€¦ (More)

We demonstrate how the novel approach to the local geometry of structures of nonholonomic nature, originated by Andrei Agrachev, works in the following two situations: rank 2 distributions of maximalâ€¦ (More)

We develop an evaluation framework for the validation of conformance checkers for the long-term preservation. The framework assesses the correctness, usability, and usefulness of the tools for threeâ€¦ (More)