manifolds — man·i·fold || mænɪfəʊld n. something made up of many different parts; one of a number of copies; pipe or chamber having a number of outlets (Mechanics) v. make copies of, duplicate adj. varied, diverse; having many different parts or… … English contemporary dictionary
Classification of manifolds — In mathematics, specifically geometry and topology, the classification of manifolds is a basic question, about which much is known, and many open questions remain. Contents 1 Main themes 1.1 Overview 1.2 Different categories and additional… … Wikipedia
Categories of manifolds — In mathematics, specifically geometry and topology, there are many different notions of manifold, with more or less structure, and corresponding notions of map between manifolds , each of which yields a different category and its own… … Wikipedia
List of manifolds — This is a list of particular manifolds, by Wikipedia page. See also list of geometric topology topics. For categorical listings see and its subcategories.Generic families of manifolds*Euclidean space, R n * n sphere, S n * n torus, T n *Real… … Wikipedia
Maps of manifolds — A Morin surface, an immersion used in sphere eversion. In mathematics, more specifically in differential geometry and topology, various types of functions between manifolds are studied, both as objects in their own right and for the light they… … Wikipedia
Congruence (manifolds) — In the theory of smooth manifolds, a congruence is the set of integral curves defined by a nonvanishing vector field defined on the manifold. Congruences are an important concept in general relativity, and are also important in parts of… … Wikipedia
Gromov's systolic inequality for essential manifolds — In Riemannian geometry, M. Gromov s systolic inequality for essential n manifolds M dates from 1983. It is a lower bound for the volume of an arbitrary metric on M, in terms of its homotopy 1 systole. The homotopy 1 systole is the least length of … Wikipedia
Calculus on Manifolds (book) — Michael Spivak s Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus (1965, ISBN 0 8053 9021 9) is a short text treating analysis in several variables in Euclidean spaces and on differentiable manifolds. The… … Wikipedia
History of manifolds and varieties — The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic… … Wikipedia
Category of manifolds — In mathematics, the category of manifolds, often denoted Man p , is the category whose objects are manifolds of smoothness class C p and whose morphisms are p times continuously differentiable maps. This is a category because the composition of… … Wikipedia
Curvature of Riemannian manifolds — In mathematics, specifically differential geometry, the infinitesimal geometry of Riemannian manifolds with dimension at least 3 is too complicated to be described by a single number at a given point. Riemann introduced an abstract and rigorous… … Wikipedia
