zbMATH — the first resource for mathematics

A test for non-compactness of the foliation of a Morse form. (English. Russian original) Zbl 0859.58005
Russ. Math. Surv. 50, No. 2, 444-445 (1995); translation from Usp. Mat. Nauk 50, No. 2, 217-218 (1995).
The author studies foliations determined by a closed 1-form with Morse singularities on smooth compact manifolds. More precisely, the author investigates the problem of the existence of a non-compact leaf, verifies a test for non-compactness of a foliation in terms of the degree of irrationality of the considered 1-form, and shows that the non-compactness of a foliation is a case of general position.

58C25 Differentiable maps on manifolds
58K99 Theory of singularities and catastrophe theory
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
Full Text: DOI