Showing papers on "Distribution (differential geometry) published in 1995"

Gas distribution through injection manifolds in vacuum systems

Abstract: When injecting gas into a vacuum system, quite often the gas is distributed through a gas injection manifold. However, designs normally rely upon practical experience. By considering the manifold arrangement as a network of flow restrictions it is possible to optimize the distribution of gas throughout the manifold. The methodology for determining the flow distribution through the two simplest topologies of gas manifold, single‐ and double‐opening manifolds from a single‐gas injection point, is derived in this article. It is shown that the double‐opening manifold topology tends to provide more uniform flow distribution than the single‐opening manifold topology for similar conductance ratios. The results of this work include a summation formula for the single‐opening manifold. In addition, guidelines for one type of tailored flow manifold are given. Finally, three basic design rules are presented: (1) use as few holes in the manifold as possible, (2) use a double opening manifold when possible, and (3) spe...

On CR-submanifolds of the six-dimensional sphere

Abstract: We consider proper CR-submanifolds of the six-dimensional sphere S6. We prove that S6 does not admit compact proper CR-submanifolds with non-negative sectional curvature and integrable holomorphic distribution.

Parallelisability conditions for differentiable three-webs

Abstract: Our aim is to nd conditions under which a 3-web on a smooth 2n-dimensional manifold is locally equivalent with a web formed by three systems of parallel n-planes in R 2n. We will present here a new approach to this \classical" problem using projectors onto the distributions of tangent subspaces to the leaves of foliations forming the web. The parallelisability conditions for multicodimensional 3-webs were at rst formulated by S.S. Chern, 3]. Later on M. A. Akivis, 1], interpreted these conditions as vanishing of both torsion and curvature tensors of a certain connection intimately related to the web, so called canonical Chern connection of a 3-web (M. Kikkawa, 8]). We will nd parallelisability conditions formulated in terms of projectors of a web, and will verify that they are equivalent with those derived by Akivis. At the same time we will show that the problem of parallelisability of a 3-web is equivalent with integrability of a (P; B)-structure (a couple of polynomial structures deening a 3-web). All objects under consideration will be supposed of the class C 1 (smooth). A 3-web on a 2n-dimensional manifold is given by a triple of foliations (in general position) of codimension n which are usually deened by totally integrable systems of Pfaaan equations. For our purposes let us choose the following deenition. Deenition 1. Under a diierentiable 3-web W on a manifold M 2n of dimension 2n we will understand here a triple W = (D 1 ; D 2 ; D 3) of (smooth) n-dimensional integrable distributions which are pairwise complementary.

On the weak integrability and the quasiasymptotics of a distribution

Abstract: We investigate the connection between the notions of the quasiasymptotics at ∞ and the weak integrability for tempered distributions supported by [0,∞).