differentiable manifold

plural differentiable manifolds · alternative differential manifold

1. differential geometryA manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus;

   The charts (homeomorphisms) that make up any differentiable structure of a differentiable manifold are required to be such that the transition from one to another is differentiable.

   3 more examples

   Whitney showed that a differentiable manifold Mᵏ can be regularly mapped on the vector space R#123;2k#125;.

   1950, L. S. Pontryagin, Characteristic Cycles on Differentiable Manifolds, American Mathematical Society, page 33

   The phase space of a dynamical system will be taken to be a differentiable manifold.

   1994, N. Aoki, K. Hiraide, Topological Theory of Dynamical Systems: Recent Advances, Elsevier (North-Holland), page 1

   In this chapter we introduce differentiable manifolds and smooth maps. A differentiable manifold' is a topological space on which there are defined coordinates allowing basic notions of differentiability.

   2009, Jeffrey Marc Lee, Manifolds and Differential Geometry, American Mathematical Society, page 1

2. A manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus; (more formally) a manifold that can be equipped with a differentiable structure (an atlas of ℝⁿ-compatible charts).
   1. differential geometry; more formallya manifold that can be equipped with a differentiable structure (an atlas of ℝⁿ-compatible charts).