The structure of the set of singular points of a codimension differential system on a -manifold

Authors:
P. Mormul and M. Ya. Zhitomirskiĭ

Journal:
Trans. Amer. Math. Soc. **342** (1994), 619-629

MSC:
Primary 58A17; Secondary 58A30, 58C27

DOI:
https://doi.org/10.1090/S0002-9947-1994-1150017-9

MathSciNet review:
1150017

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Abstract: Generic modules *V* of vector fields tangent to a 5-dimensional smooth manifold *M*, generated locally by four not necessarily linearly independent fields , , , , are considered. Denoting by the 1-form conjugated to *V* ( is a fixed local volume form on *M*), the loci of singular behavior of and are handled. The local classification of this pair of sets is carried out (outside a curve and a discrete set in ) up to a smooth diffeomorphism. In the most complicated case, around points of a codimension 3 submanifold of *M*, turns out to be diffeomorphic to the Cartesian product of and the Whitney's umbrella in .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1150017-9

Keywords:
Differential system,
class of Pfaffian equation,
Morse lemma with parameters

Article copyright:
© Copyright 1994
American Mathematical Society