Generic aspects of the geometry of leaves of foliations
نویسندگان
چکیده
A leaf of a compact foliated space has a well defined quasi-isometry type and it is a natural question to ask which quasi-isometry types of (intrinsic) metric spaces can appear as leaves of foliated spaces. There are two more or less related concepts of quasi-isometry. The first one is that used in Riemannian geometry, namely, two (Lipschitz) manifolds are quasi-isometric if there is a Lipschitz homeomorphism f : X → Y. The more general concept is that in which twometric spaces X,Y are coarsely quasi-isometric if there is a mapping f : X → Y such that
منابع مشابه
On the k-nullity foliations in Finsler geometry
Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$-forms on the bundle of non-zero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$-nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive...
متن کاملIdentification of Riemannian foliations on the tangent bundle via SODE structure
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...
متن کاملFibrations, Divisors and Transcendental Leaves
We will use flat divisors, and canonically associated singular holomorphic foliations, to investigate some of the geometry of compact complex manifolds. The paper is mainly concerned with three distinct problems: the existence of fibrations, the topology of smooth hypersurfaces and the topological closure of transcendental leaves of foliations.
متن کاملMetrics and Smooth Uniformisation of Leaves of Holomorphic Foliations
We consider foliations of complex projective manifolds by analytic curves. In a generic case each leaf is hyperbolic and there exists unique Poincaré metric on the leaves. It is shown that in a generic case this metric smoothly depends on a leaf. The manifold of universal covering of the leaves passing through some transversal base has a natural complex structure. It is shown that this structur...
متن کاملThematization Strategies in the Generic Moves of Research Article Introductions
Despite the heterogeneity of ideas regarding the definitions of genre, there are also common instances shared among scholars interested in particular aspects of the notion. Swales (1990) and Bhatia (1993) are primarily interested in the sociological and psychological aspects of genre's functioning and construction, respectively.. Swales analyzes the genre of 'article introduction', into four ge...
متن کامل