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Singularities and normal forms of smooth distributions. (English) Zbl 0841.58005
Jakubczyk, Bronisław (ed.) et al., Geometry in nonlinear control and differential inclusions. Proceedings of the workshop on differential inclusions held May 17-29, 1993 and the workshop on geometry in nonlinear control, May 31-June 25, 1993 in Warsaw, Poland. Warsaw: Polish Academy of Sciences, Banach Cent. Publ. 32, 395-409 (1995).
A smooth $$k$$-distribution is a $$k$$-dimensional subbundle of the tangent bundle $$TM^n$$. Locally it means a $$k$$-generated module of vector fields on $$M^n$$ or a $$(n - k)$$-generated module of $$l$$-forms. Two $$k$$-distributions are equivalent when for the $$k$$-generated modules $$V$$ and $$V'$$ defining them there exists a local diffeomorphism $$\varphi$$ such that $$\varphi_* V = V'$$. The author presents old and new results on local classification of $$k$$-distributions. A special attention is paid to the nonclassical cases $$2 \leq k \leq n-2$$, $$(k,n) = (2,4)$$ as well as to the circumstancies when singularities appear. A very good expository paper.
For the entire collection see [Zbl 0827.00041].

##### MSC:
 58A30 Vector distributions (subbundles of the tangent bundles)
##### Keywords:
smooth distributions; normal forms; singularities