Displaying similar documents to “Close cohomologous Morse forms with compact leaves”

On the structure of a Morse form foliation

I. Gelbukh (2009)

Czechoslovak Mathematical Journal

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The foliation of a Morse form ω on a closed manifold M is considered. Its maximal components (cylinders formed by compact leaves) form the foliation graph; the cycle rank of this graph is calculated. The number of minimal and maximal components is estimated in terms of characteristics of M and ω . Conditions for the presence of minimal components and homologically non-trivial compact leaves are given in terms of rk ω and Sing ω . The set of the ranks of all forms defining a given foliation without...

The Poincaré-Bendixson theorem and arational foliations on the sphere

Igor Nikolaev (1996)

Annales de l'institut Fourier

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Foliations on the 2-sphere with a finite number of non-orientable singularities are considered. For this class a Poincaré-Bendixson theorem is established. In particular, the work gives an answer to a problem of H. Rosenberg concerning labyrinths.