Dictionary

differentiable manifold en · NOUN

Meanings

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

Forms

Translations (7)

bg диференцируемо многообразие (manifold locally similar enough to a Euclidean space for calculus to be done) · fr variété différentiable (manifold locally similar enough to a Euclidean space for calculus to be done) · fr variété différentielle (manifold locally similar enough to a Euclidean space for calculus to be done) · de differenzierbare Mannigfaltigkeit (manifold locally similar enough to a Euclidean space for calculus to be done) · it varietà differenziabile (manifold locally similar enough to a Euclidean space for calculus to be done) · pl rozmaitość różniczkowa (manifold locally similar enough to a Euclidean space for calculus to be done) · pl rozmaitość różniczkowalna (manifold locally similar enough to a Euclidean space for calculus to be done)