Topic
Distribution (differential geometry)
About: Distribution (differential geometry) is a research topic. Over the lifetime, 911 publications have been published within this topic receiving 10149 citations.
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TL;DR: In this paper, the authors investigated the distribution of orbits of a non-elementary discrete hyperbolic subgroup Γ acting on ℍn and its geometric boundary.
Abstract: We investigate the distribution of orbits of a non-elementary discrete hyperbolic subgroup Γ acting on ℍn and its geometric boundary ∂∞(ℍn). In particular, we show that if Γ admits a finite Bowen–Margulis–Sullivan measure (for instance, if Γ is geometrically finite), then every Γ-orbit in ∂∞(ℍn) is equidistributed with respect to the Patterson–Sullivan measure supported on the limit set Λ(Γ). The appendix by Maucourant is the extension of a part of his PhD thesis where he obtains the same result as a simple application of Roblin’s theorem. Our approach is via establishing the equidistribution of solvable flows on the unit tangent bundle of Γ∖ℍn, which is of independent interest.
25 Jun 2008
TL;DR: In this article, a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and structures connected with the Frobenius integrability/nonintegrability theorems given in terms of distributions on manifolds with corresponding curvature defined by the Nijenhuis operator is presented.
Abstract: This paper aims to present a general idea for description of spatially finite physical objects with a consistent nontrivial translational-rotational dynamical structure and evolution as a whole, making use of the mathematical concepts and structures connected with the Frobenius integrability/nonintegrability theorems given in terms of distributions on manifolds with corresponding curvature defined by the Nijenhuis operator. The idea is based on consideration of nonintegrable subdistributions of some appropriate completely integrable distribution (differential system) on a manifold and then to make use of the corresponding curvatures as generators of measures of interaction, i.e. of energy-momentum exchange among the physical subsystems mathematically represented by the nonintegrable subdistributions. The concept of photon-like object is introduced and description of such objects in these terms is given.
Patent•
02 Apr 2020
TL;DR: In this paper, the authors describe a system for holding workpieces in place during processing using a distribution manifold coupled to a vacuum source, and multiple linear valves coupled to the distribution manifold, where each linear valve has a manifold with multiple openings and is adjustable to select one or more of the multiple openings to have a path to the vacuum source through the manifold.
Abstract: Aspects of a system for holding workpieces in place during processing are described. In an example, the system includes a distribution manifold coupled to a vacuum source, and multiple linear valves coupled to the distribution manifold, where each linear valve has a manifold with multiple openings and is adjustable to select one or more of the multiple openings to have a path to the vacuum source through the distribution manifold for providing a vacuum to hold a workpiece in place. In another example, the system includes a vacuum holder having a first array of openings, a system of linear valves positioned below the vacuum holder and having a second array of openings that aligns with the first array of openings, and a vacuum source that provides vacuum for holding a workpiece on the vacuum holder. A method for holding workpieces in place during processing using these systems is also described.
TL;DR: In this paper, it was shown that any Kahler manifold admitting a flat complex conformal connection is a Bochner-Kahler manifold with special scalar distribution and zero geometric constants.
Abstract: We prove that any Kahler manifold admitting a flat complex conformal connection is a Bochner-Kahler manifold with special scalar distribution and zero geometric constants. Applying the local structural theorem for such manifolds we obtain a complete description of the Kahler manifolds under consideration.
01 Jan 2013
TL;DR: In this paper, the integrability of various distributions of GCR-light-like submanifolds of an indefinite Kenmotsumanifold was studied and necessary and sufficient conditions for the integrinability of these distributions were given.
Abstract: We give necessary and sufficient conditions for the integrability ofvarious distributions of GCR-lightlike submanifold of an indefinite Kenmotsumanifold. We also find the conditions for each leaf of holomorphic distributionand radical distribution to be totally geodesic in submanifold