Mathematics – Differential Geometry
Scientific paper
2010-11-08
Mathematics
Differential Geometry
Scientific paper
In the recent years, a number of issues concerning distributions generating 1- flags (called also Goursat flags) has been analyzed. Presently similar questions are discussed as regards distributions generating multi-flags. (In fact, only so-called special multi-flags, to avoid functional moduli.) In particular and foremost, special 2-flags of small lengths are a natural ground for the search of generalizations of theorems established earlier for Goursat objects. In the present paper we locally classify, in both C{\omega} and C \infty categories, special 2-flags of lengths not exceeding four. We use for that the known facts about special multi-flags along with fairly recent notions like strong nilpotency of distributions. In length four there are already 34 orbits, the number to be confronted with only 14 singularity classes - basic invariant sets discovered in 2003. As a common denominator for different parts of the paper, there could serve the fact that only rarely multi-flags' germs are strongly nilpotent, whereas all of them are weakly nilpotent, or nilpotentizable (possessing a local nilpotent basis of sections).
Mormul Piotr
Pelletier Fernand
No associations
LandOfFree
Special 2-flags in lengths not exceeding four: a study in strong nilpotency of distributions 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 Special 2-flags in lengths not exceeding four: a study in strong nilpotency of distributions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Special 2-flags in lengths not exceeding four: a study in strong nilpotency of distributions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-131048