1.NounA manifold that is locally similar enough to a Euclidean space (ℝ) to allow one to do calculus; a manifold that can be equipped with a differentiable structure (an atlas of ℝ-compatible charts).
"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."