Mathematics – Differential Geometry
Scientific paper
2006-05-02
Mathematics
Differential Geometry
13 pages
Scientific paper
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.
Agrachev Andrei
Zelenko Igor
No associations
LandOfFree
Nurowski's conformal structures for (2,5)-distributions via dynamics of abnormal extremals does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Nurowski's conformal structures for (2,5)-distributions via dynamics of abnormal extremals, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nurowski's conformal structures for (2,5)-distributions via dynamics of abnormal extremals will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-184452