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: A fast manifold learning strategy to estimate the underlying geometrical distribution and develop the relevant mathematical criterion on the basis of the extreme learning machine (ELM) in the high-dimensional space is proposed.
22 citations
01 Jan 1998
TL;DR: In this paper, the integrability condition of the distribution on semi-invariant submanifolds of LP-Sasakian manifold is studied, where the authors consider the Lorentzian para contact structure.
Abstract: Recently Matsumoto (1) introduced the idea of Lorentzian para contact structure and studied its several properties. In the present paper we studied the integrability condition of the distribution on semi-invariant submanifolds of LP-Sasakian manifold. p p p
22 citations
TL;DR: In this paper, the integrability of non-closed distributions on Banach manifolds was studied and the notion of weak distribution was introduced and conditions under which these distributions admit weak integral submanifolds.
22 citations
TL;DR: The Walczak formula is a very nice tool for understanding the geometry of a Riemannian manifold equipped with two orthogonal complementary distributions as discussed by the authors, and it simplifies to a Bochner-type formula when dealing with Kahler manifolds and holomorphic (integrable) distributions.
22 citations
TL;DR: In this article, the authors characterize the smooth families of maps where the topological dynamics does not change (the smooth deformations) as the families tangent to a continuous distribution of codimension-one subspaces (the "horizontal" directions) in that space.
Abstract: In the space of $C^k$ piecewise expanding unimodal maps, $k\geq 1$, we characterize the $C^1$ smooth families of maps where the topological dynamics does not change (the "smooth deformations") as the families tangent to a continuous distribution of codimension-one subspaces (the "horizontal" directions) in that space. Furthermore such codimension-one subspaces are defined as the kernels of an
explicit class of linear functionals. As a consequence we show the existence of $C^{k-1+Lip}$ deformations tangent to every given $C^k$ horizontal direction, for $k\ge 2$.
22 citations