Showing papers on "Distribution (differential geometry) published in 1999"

Manifold system of removable components for distribution of fluids

Abstract: A manifold system for enabling a distribution of fluids includes a plurality of individual manifold blocks that can be joined together to form a gas stick. Each manifold block will have a fluid passage way with an entrance port and exit port accessing a common surface. An active component can be mounted to one manifold block, while extending across a port of an adjacent manifold block. An alignment system can be provided to ensure that the entrance and exit ports are positioned in a plane containing the common surface to facilitate sealing.

An intrinsic definition of the Colombeau generalized functions

Abstract: A slight modification of the definition of the Colombeau generalized functions allows to have a canonical embedding of the space of the distributions into the space of the generalized functions on a C∞ manifold. The previous attempt in [5] is corrected, several equivalent definitions are presented.

Hölder regularity of horocycle foliations

Abstract: Let M be a C∞, nonpositively curved manifold. A horosphere in M is the projection to M of a limit of metric spheres in the universal cover M (see §2). A horospherical foliation H is a foliation of the unit tangent bundle T 1M whose leaves consist of unit normal vector fields to horospheres.1 While regularity of horospherical foliations has been studied extensively for negatively curved manifolds M , considerably less is known in the nonpositively curved case. The most general result is due to P. Eberlein: if M is complete and nonpositively curved, then horospheres are C2, which implies that the individual leaves of H are C1. Further, the tangent distribution TH depends continuously the basepoint v ∈ T 1M (see [9]). Beyond Eberlein’s theorem, smoothness results have consisted mainly of counterexamples ([2],[5]); in particular, the best one could hope for in the case of a general compact, nonpositively curved M is for TH to be Holdercontinuous. In this paper we prove

On the vertical bundle of a pseudo-Finsler manifold

Abstract: We define the Liouville distribution on the tangent bundle of a pseudo-Finsler manifold and prove that it is integrable. Also, we find geometric properties of both leaves of Liouville distribution and the vertical distribution.

Variational aspects of the geodesic problem in sub-Riemannian geometry

Abstract: We study the local geometry of the space of horizontal curves with endpoints freely varying in two given submanifolds $\mathcal P$ and $\mathcal Q$ of a manifold $\mathcal M$ endowed with a distribution $\mathcal D\subset T\M$. We give a different proof, that holds in a more general context, of a result by Bismut (Large Deviations and the Malliavin Calculus, Birkhauser, 1984) stating that the normal extremizers that are not abnormal are critical points of the sub-Riemannian action functional. We use the Lagrangian multipliers method in a Hilbert manifold setting, which leads to a characterization of the abnormal extremizers (critical points of the endpoint map) as curves where the linear constraint fails to be regular. Finally, we describe a modification of a result by Liu and Sussmann that shows the global distance minimizing property of sufficiently small portions of normal extremizers between a point and a submanifold.

Stochastic equations and quasi-invariance on infinite product groups

Abstract: A stochastic differential equation on an infinite-dimensional Lie group G constructed as the countable power of a compact Lie group G is considered. The existence and uniqueness of the solutions and quasi-invariance of their distribution are proved.

Distribution Phenomena in Continued Fractions and Logistic Map

Abstract: We have been studying chaotic behavior and chaos-like behavior in continued fractions. In this paper, such chaos-like behavior is investigated in detail. This behavior originates in the complex numbers that determine the Cauchy distributions, where cyclic terms discretely appear at isolated parameter values. The distributions are formed along with alternate tangent functions that are dominated by the cyclic terms characterized by double-Markov processes. Finally, the probability densities of the logistic map are analyzed based on the Cauchy distributions, like state density calculations in solids.

On four-dimensional three-webs with integrable transversal distributions

Abstract: For a four-dimensional (nonisoclinicly geodesic) three-web W (3, 2, 2), a transversal distribution $\Delta$ is defined by the torsion tensor of the web. In general, this distribution is not integrable. The authors find necessary and sufficient conditions of its integrability and prove the existence theorem for webs W (3, 2, 2) with integrable distributions $\Delta$. They prove that for a web W (3, 2, 2) with the integrable distribution $\Delta$, the integral surfaces $V^2$ of $\Delta$ are totally geodesic in an affine connection of a certain bundle of affine connections. They also consider a class of webs W (3, 2, 2) for which the integral surfaces $V^2$ of $\Delta$ are geodesicly parallel with respect to the same affine connections and a class of webs for which two-dimensional webs W (3, 2, 1) cut by the foliations of W (3, 2, 2) on $V^2$ are hexagonal. They prove the existence theorems for webs of the latter class as well as for webs of the subclass which is the intersection of two classes mentioned above. The authors also establish relations between three-webs considered in the paper.

Intrinsic normalizations of a hyperplane distribution on the grassmann manifold. II

Abstract: We consider intrinsic normalizations of a hyperplane distribution on the Grassmann manifold of ann-dimensional projective space.