Finite type Monge–Ampère foliations

Finite Energy Foliations on Overtwisted Contact Manifolds

We develop a method for preserving pseudoholomorphic curves in contact 3–manifolds under surgery along transverse links. This makes use of a geometrically natural boundary value problem for holomorphic curves in a 3–manifold with stable Hamiltonian structure, where the boundary conditions are defined by 1–parameter families of totally real surfaces. The technique is applied here to construct a ...

Leaves of Foliations with a Transverse Geometric Structure of Finite Type

ROBERT A. WOLAK In Chis short note we find some conditions which ensure that a G foliation of finite type with all leaves compact is a Riemannian foliation or equivalently the space of leaves of such a foliation is a Satake manifold . A particular attention is paid to transversely affine foliations . We present several conditions such ensure completeness of these foliations . In this short note...

Laminations and Flows Transverse to Finite Depth Foliations

Liouville-type theorems for foliations with complex leaves

In this paper we discuss some structure problems regarding the foliation of Levi flat manifolds, i.e. those CR manifolds which are foliated by complex leaves or, equivalently, whose Levi form vanishes. Levi flat manifolds have a particular significance among CR manifolds, since due to their degenerate nature they often behave as “limit case”, or they are an obstruction in extension problems of ...

Hyperpolar Homogeneous Foliations on Symmetric Spaces of Noncompact Type

Abstract. A foliation F on a Riemannian manifold M is hyperpolar if it admits a flat section, that is, a connected closed flat submanifold of M that intersects each leaf of F orthogonally. In this article we classify the hyperpolar homogeneous foliations on every Riemannian symmetric space M of noncompact type. These foliations are constructed as follows. Let Φ be an orthogonal subset of a set ...