We prove that a Morse type codimension one holomorphic foliation is not transverse to a sphere in the complex affine space. Also we characterize the variety of contacts of a linear foliation with concentric spheres.

The cerebellum consists of an intricate array of lobules that arises during the process of foliation. Foliation not only increases surface area, but may also facilitate organization of cerebellar neural circuitry. Defects in cerebellar foliation are associated with a number of diseases. Yet, little is known about how foliation, a process involving large-scale and simultaneous movement of severa...

conclusions the modified illinois change of direction test must be considered as an asymmetrical test because it underestimates more than half of the players’ agility performances. therefore, fitness coaches should take these results into account when using this test. results the analysis revealed no significant difference in time performance between the two versions of test as a within-subject...

Let F be a codimension one foliation on a closed manifold M which admits a transverse dimension one Riemannian foliation. Then any continuous leafwise harmonic functions are shown to be constant on leaves.

We prove that a codimension one foliation of an orientable paracompact manifold has at most a countable number of nonorientable leaves. We also give an example of a codimension one foliation of a compact orientable manifold with an infinite number of nonorientable leaves. Introduction. The purpose of this paper is to investigate the occurrence of nonorientable leaves in a codimension one foliat...

15 3. Stable and unstable filtrations 17 3.1. Existence and subfoliation 17 3.2. Absolute continuity 19 4. Central Foliations 21 4.1. Normal hyperbolicity 21 4.2. Integrability of the central foliation and dynamical coherence 23 4.3. Smoothness of central leaves via normal hyperbolicity 25 4.4. Robustness of the central foliation 26 5. Intermediate Foliations 27 5.1. Nonintegrability of interme...

We study some kind of rigidity property for dicritical foliation in C 2 thanks to a new meromorphic function associated to any dicriti-cal foliation playing the role of equation of separatrix. To be more specific, we compute infinitesimal obstructions for realizing the holon-omy pseudo-group of a dicritical foliation F on any source manifold of a blowing-up morphism with same dual tree as the d...

In this paper we reduce the Poincaré Problem for foliations in P to a problem of postulation of plane curves of degree m − 1, with m denoting the degree of the foliation. In the cases in which we can assure a solution for the Poincaré Problem the bound for the degree of the first integral depends only on the degree of the foliation. An intermediate result gives a solution for Painlevé’s Problem...