Structural stability theorems for integrable differential forms on 3-manifolds

Ahlfors Theorems for Differential Forms

and Applied Analysis 3 Let y1, . . . , yk be an orthonormal system of coordinates in R, 1 ≤ k ≤ n. Let A be a domain in R, and let B be an n − k -dimensional Riemannian manifold. We consider the manifold N A × B. 2. Boundary Sets Below we introduce the notions of parabolic and hyperbolic type of boundary sets on noncompact Riemannian manifolds and study exhaustion functions of such sets. We als...

Markov Theorems for Links in 3-manifolds

We describe here a Markov theorem for links in S 2 S 1 using the braid groups corresponding to the Coxeter groups of type B l. See the theorem in x3. We will work on a more general setting. The only reason here to single out S 2 S 1 is its simplicity. It is possible that all the other Artin groups will turn out to be useful in the study of links in 3-manifolds.

3-manifolds Admitting Toric Integrable Geodesic Flows

A toric integrable geodesic flow on a manifold M is a completely integrable geodesic flow such that the integrals generate a homogeneous torus action on the punctured cotangent bundle T ∗M \ M . A toric integrable manifold is a manifold which has a toric integrable geodesic flow. Toric integrable manifolds can be characterized as those whose cosphere bundle (the sphere bundle in the cotangent b...

Stability theorems for some functional differential equations

On the Local Stability of Differential Forms

In this paper we determine which germs of differential îforms on an n-manifold are stable (in the sense of Martinet). We show that when s ¥= 1 or when 4=1 and n < 4 Martinet had found almost all of the possible examples. The most interesting result states that for certain generic singularities of 1-forms on 4-manifolds an infinite dimensional moduli space occurs in the classification of the 1-f...