differentiable manifold
noun1
A manifold that is locally similar enough to a Euclidean space (ℝⁿ) to allow one to do calculus;
Differential geometry
- 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.
- 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:
2 more examples
- 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:
› A manifold that is locally similar enough to…
2
a manifold that can be equipped with a differentiable structure (an atlas of ℝⁿ-compatible charts).
Differential geometry; more formally