As was shown recently by P. Nurowski, to any rank 2 maximally nonholonomic
vector distribution on a 5-dimensional manifold M one can assign the canonical
conformal structure of signature (3,2). His construction is based on the
properties of the special 12-dimensional coframe bundle over M, which was
distinguished by E. Cartan during his famous construction of the canonical
coframe for this type of distributions on some 14-dimensional principal bundle
over M. The natural question is how "to see" the Nurowski conformal structure
of a (2,5)-distribution purely geometrically without the preliminary
construction of the canonical frame. We give rather simple answer to this
question, using the notion of abnormal extremals of (2,5)-distributions and the
classical notion of the osculating quadric for curves in the projective plane.
Our method is a particular case of a general procedure for construction of
algebra-geometric structures for a wide class of distributions, which will be
described elsewhere. We also relate the fundamental invariant of
(2,5)-distribution, the Cartan covariant binary biquadratic form, to the
classical Wilczynski invariant of curves in the projective plane.Comment: 13 page