A test for non-compactness of the foliation of a Morse form. (English. Russian original) Zbl 0859.58005

Mel’nikova, I. A.

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.

Reviewer: N.Papaghiuc (Iaşi)

MSC:

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

Keywords:

Morse form; foliations; non-compactness