Special 2-flags in lengths not exceeding four: a study in strong nilpotency of distributions
Year: 2010
Type: preprint
Abstract: In the recent years, a number of issues concerning distributions generating 1flags (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 ! and C 1 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).
Source: arXiv (Cornell University)
Author: Fernand Pelletier
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1657210274