Showing papers on "Distribution (differential geometry) published in 1991"
TL;DR: In this paper, a contact structure on a (2 n + l)-dimensional manifold M is a maximally non-integrable hyperplane distribution D in the tangent bundle TM, i.e., D is locally denned as the kernel of a 1-form α satisfying α ۸ (da) n ہ 0.
Abstract: All manifolds in this paper are assumed to be closed, oriented and smooth. A contact structure on a (2 n + l)-dimensional manifold M is a maximally non-integrable hyperplane distribution D in the tangent bundle TM, i.e., D is locally denned as the kernel of a 1-form α satisfying α ۸ (da) n ۸ 0. A global form satisfying this condition is called a contact form. In the situations we are dealing with, every contact structure will be given by a contact form (see [5]). A manifold admitting a contact structure is called a contact manifold.
57 citations
TL;DR: A new approach to effect the transition between local and global representations is presented, based on the notion of a covering, or a collection of objects whose union is equivalent to the full one, which is defined by the union of the local dynamic curves.
Abstract: We present a new approach to effect the transition between local and global representations. It is based on the notion of a covering, or a collection of objects whose union is equivalent to the full one. The mathematics of computing global coverings are developed in the context of curve detection, where an intermediate representation (the tangent field) provides a reliable local description of curve structure. This local information is put together globally in the form of a potential distribution. The elements of the covering are then short curves, each of which evolves in parallel to seek the valleys of the potential distribution. The initial curve positions are also derived from the tangent field, and their evolution is governed by variational principles. When stationary configurations are achieved, the global dynamic covering is defined by the union of the local dynamic curves.
41 citations
TL;DR: In this paper, small-time local controllability of a C1 affine control system with a generic drift vector field and n − 1 linearly independent input vector fields on an n-dimensional connected C1 manifold was studied, showing that a necessary condition, namely the drift vector fields belonging to the convex hull of the control vector fields at a given point, is also sufficient on an open dense subset H1 of the set of points where it is verified.
5 citations
2 citations