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February 2005 Real moduli in local classification of Goursat flags
Piotr MORMUL
Hokkaido Math. J. 34(1): 1-35 (February 2005). DOI: 10.14492/hokmj/1285766199

Abstract

Goursat distributions are subbundles (of codimension at least 2) in the tangent bundles to manifolds having the flag of consecutive Lie squares of ranks not depending on a point and growing -- very slowly -- always by 1. This defining condition is rather strong, implying local polynomial pseudo-normal forms for them (proposed in 1981 by Kumpera and Ruiz) featuring only real parameters of ${\it à}$ ${\it priori}$ unknown status, many of them reducible by further diffeomorphisms of the base manifold. We show that in the local ${\rm C}^\infty$ and ${\rm C}^{\omega}$ classifications of Goursat distributions genuine continuous moduli appear already in codimension 2. First examples of such moduli were given in codimension 3; in codimensions 0 and 1 the local classification is known and discrete.

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Piotr MORMUL. "Real moduli in local classification of Goursat flags." Hokkaido Math. J. 34 (1) 1 - 35, February 2005. https://doi.org/10.14492/hokmj/1285766199

Information

Published: February 2005
First available in Project Euclid: 29 September 2010

zbMATH: 1074.58001
MathSciNet: MR2130770
Digital Object Identifier: 10.14492/hokmj/1285766199

Subjects:
Primary: 58A30
Secondary: 58A17

Rights: Copyright © 2005 Hokkaido University, Department of Mathematics

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Vol.34 • No. 1 • February 2005
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