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.

A Three-Generation Calabi-Yau Manifold with Small Hodge Numbers

Abstract: We present a complete intersection Calabi-Yau manifold Y that has Euler number -72 and which admits free actions by two groups of automorphisms of order 12. These are the cyclic group Z_12 and the non-Abelian dicyclic group Dic_3. The quotient manifolds have chi=-6 and Hodge numbers (h^11,h^21)=(1,4). With the standard embedding of the spin connection in the gauge group, Y gives rise to an E_6 gauge theory with 3 chiral generations of particles. The gauge group may be broken further by means of the Hosotani mechanism combined with continuous deformation of the background gauge field. For the non-Abelian quotient we obtain a model with 3 generations with the gauge group broken to that of the standard model. Moreover there is a limit in which the quotients develop 3 conifold points. These singularities may be resolved simultaneously to give another manifold with (h^11,h^21)=(2,2) that lies right at the tip of the distribution of Calabi-Yau manifolds. This strongly suggests that there is a heterotic vacuum for this manifold that derives from the 3 generation model on the quotient of Y. The manifold Y may also be realised as a hypersurface in the toric variety. The symmetry group does not act torically, nevertheless we are able to identify the mirror of the quotient manifold by adapting the construction of Batyrev.

Limiting angle of brownian motion in certain two-dimensional Cartan-Hadamard manifolds

Abstract: Suppose that IH is a two-dimensional Cartan-Hadamard manifold with sectional curvatures satisfying a weak negative upper bound and no lower bound. Then the angular part of Brownian motion on IH tends to a limit as time tends to the explosion time of the Brownian motion. Moreover this limit angle has a distribution whose closed support is dense on the circle at infinity. KEY-WORDS : Brownian motion, Cartan-Hadamard manifold, comparison arguments, geodesic, limiting angle, sectional curvature, stochastic differential equations. Subject Classification 60J65, 58G32

Bi-paracontact structures and Legendre foliations

Abstract: We study almost bi-paracontact structures on contact manifolds. We prove that if an almost bi-paracontact structure is defined on a contact manifold (M, η), then under some natural assumptions of integrability M carries two transverse bi-Legendrian structures. Conversely, if two transverse bi-Legendrian structures are defined on a contact manifold, then M admits an almost bi-paracontact structure. We define a canonical connection on an almost bi-paracontact manifold and we study its curvature properties, which resemble those of the Obata connection of a para-hypercomplex (or complex-product) manifold. Further, we prove that any contact metric manifold whose Reeb vector field belongs to the (κ, μ)-nullity distribution canonically carries an almost bi-paracontact structure and we apply the previous results to the theory of contact metric (κ, μ)-spaces.

Low thermal stress steam distribution manifold

Abstract: A manifold for dividing a single, two-phase mixed stream of vapor and liquid into a plurality of individual streams of substantially uniform quality. The manifold includes: a flow disperser having an inlet port for receiving the vapor-liquid mixture and at least two outlet ports; at least two hollow runners, each runner having a first end in fluid communication with one of the outlet ports of the flow disperser and a second end; a substantially toroidal manifold shell having at least two fluid receiver ports in fluid communication with each of the second ends of the runners, the manifold shell defining a manifold chamber; and a plurality of distribution ports spaced about the toroidal manifold shell, the distribution ports located on the toroidal manifold shell in a substantially coplanar relationship with the fluid receiver ports, each distribution port in fluid communication with the manifold chamber of the toroidal manifold shell; wherein the vapor-liquid mixture emanating from each the distribution port of the manifold is of substantially uniform quality. A method for uniformly distributing a vapor-liquid mixture is also provided.

Integrability of weak distributions on Banach manifolds

Abstract: This paper concerns the problem of integrability of non closed distributions on Banach manifolds. We introduce the notion of weak distribution and we look for conditions under which these distributions admit weak integral submanifolds. We give some applications to Banach Lie algebroid and Banach Lie-Poisson manifold. The main results of this paper generalize the works presented in [ChSt], [Nu] and [Gl].