On graphical foliations and the global existence of Euler's multiplier

Details On graphical foliations and the global existence of Euler's multiplier On graphical foliations and the global existence of Euler's multiplier

2001-08-22

arxiv.org/abs/math/0108153v2

Mathematics

Geometric Topology

28 pages, 10 figures; some sections added or completely rewritten

Scientific paper

We present an equivalent criterion for the global existence of Euler's multiplier for an integrable one-form taking into account the corresponding codim-1-foliation. In particular, the impact of inseparable leaves is considered. Here, we suppose that the foliation can be reduced to a graph; we also discuss obstructions for this assumption. The properties of this graph are decisive for the global existence of Euler's multiplier. As applications we investigate some special cases in which the graph turns out to look very simple.

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