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, a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors; and the Hormander's bracket condition for real vector fields was given.
Abstract: We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors; and the Hormander's bracket condition for real vector fields. Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators. Finally we describe a class of compact homogeneous CR manifolds for which the distribution of (0,1) vector fields satisfies a subelliptic estimate.
4 citations
TL;DR: In this article, the authors prove a Goldberg-Sachs theorem in dimension three for the existence of a null line distribution whose orthogonal complement is integrable and totally geodetic.
Abstract: We prove a Goldberg-Sachs theorem in dimension three. To be precise, given a three-dimensional Lorentzian manifold satisfying the topological massive gravity equations, we provide necessary and sufficient conditions on the tracefree Ricci tensor for the existence of a null line distribution whose orthogonal complement is integrable and totally geodetic. This includes, in particular, Kundt spacetimes that are solutions of the topological massive gravity equations.
4 citations
TL;DR: In this article, a simple model mirroring the essential aspects of this interaction is shown to generate perennial out of equilibrium condition, intermittency and 1 / f -noise, with an inverse power law distribution of waiting times.
Abstract: We discuss a route to intermittency based on the concept of reflexivity, namely on the interaction between observer and stochastic reality. A simple model mirroring the essential aspects of this interaction is shown to generate perennial out of equilibrium condition, intermittency and 1 / f -noise. In the absence of noise the model yields a symmetry-induced equilibrium manifold with two stable states. Noise makes this equilibrium manifold unstable, with an escape rate becoming lower and lower upon time increase, thereby generating an inverse power law distribution of waiting times. The distribution of the times of permanence in the basin of attraction of the equilibrium manifold are analytically predicted through the adoption of a first-passage time technique. Finally we discuss the possible extension of our approach to deal with the intermittency of complex systems in different fields.
4 citations
TL;DR: In this article, the authors obtained special framings adapted to a geometry of rays satisfying a set of equations which are similar to Cartan's equations for Cauchy-Riemann spaces.
4 citations
01 Dec 1986
TL;DR: In this article, the existence of feedback feedback such that the space of leaves is a Hausdorff manifold is discussed, and sufficient conditions for the foliation of leaves are derived from the view point of characteristic classes of foliations.
Abstract: Consider the nonlinear system x = f(x) + ?m i=1 gi (x) ui and the nonsingular involutive distribution ? Here we discuss the existance of feedback (?, s) such that [f + g?, ?] ? ? and [gs, ?] ? ?. Single input case is given special attention, and we derive a necessary condition from the view point of characteristic classes of foliations. We give some sufficient conditions in the more general case when the foliation of ? is such that the space of leaves is a Hausdorff manifold.
4 citations