the geometry of a system of second order differential equations is the geometry of a semispray, which is a globally defined vector field on tm. the metrizability of a given semispray is of special importance. in this paper, the metric associated with the semispray s is applied in order to study some types of foliations on the tangent bundle which are compatible with sode structure. indeed, suff...

In recent years the graph of a foliation, an object which has been known for a long time, cf. 10], has known new interest. In fact there are two groupoids associated with a foliation, the homotopy groupoid and the holonomy groupoid, sometimes called the graph. It serves as a basis for the construction of the C-algebra associated to the foliation. Moreover, the homotopy groupoid of the character...

We consider the lift of a foliation to its conormal bundle and some transverse geometrical structures associated with this foliation are studied. We introduce a good vertical connection on the conormal bundle and, moreover, if the conormal bundle is endowed with a transversal Cartan metric, we obtain that the lifted foliation to its conormal bundle is a Riemannian one. Also, some transversally ...

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...

Across the brains of different bird species, the cerebellum varies greatly in the amount of surface folding (foliation). The degree of cerebellar foliation is thought to correlate positively with the processing capacity of the cerebellum, supporting complex motor abilities, particularly manipulative skills. Here, we tested this hypothesis by investigating the relationship between cerebellar fol...

1 We show that, for any regular Poisson manifold, there is an injective natural linear map from the first leafwise cohomology space into the first Poisson cohomology space which maps the Reeb class of the symplectic foliation to the modular class of the Poisson manifold. The Riemannian interpretation of those classes will permit us to show that a regular Poisson manifold whose symplectic foliat...

new structural, metamorphic, finite strain and kinematic vorticity data for granitic gneiss and metavolcano-sedimentary rocks of thetanumaharea in the arabian shield in saudi arabia reveal a history of deformation reflecting different tectonic regimes. kinematic analysis shows their relationship to the nappe contacts between the granitic gneiss and metavolcano-sedimentary rocks and explains the...

Given a transversely projective foliation F on a C∞ manifold M and a nonnegative integer k, a transversal differential operator DF (2k + 1) of order 2k + 1 from N⊗k to N⊗(−k−1) is constructed, where N denotes the normal bundle for the foliation. There is a natural homomorphism from the space of all infinitesimal deformations of the transversely projective foliation F to the first cohomology of ...

Roussarie and Thurston [Ro], [Th] showed that given a taut foliation F and an incompressible torus T in a 3-manifold M , the torus may be isotoped so that it is either transverse to the leaves of the foliation, or is equal to one of the leaves of the foliation. This result was known to be false in the more general context of a foliation F without Reeb components. The only obstruction, however [...