Definition:Differentiable Manifold
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This page is about spaces with a differentiable structure. For other uses, see Definition:Manifold.
Definition
A $C^k$ (resp. $C^\infty$, resp. complex analytic) manifold of dimension $d$ consists of
- 1. A second countable locally Euclidean space $M$ of dimension $d$
- 2. A differentiable structure $\mathscr F$ on $M$ of class $C^k$ (resp. $C^\infty$, resp. complex analytic).
When the differentiable structure is clear from the context then one often simply speaks of the manifold $M$.
A $C^\infty$ manifold is also called a smooth manifold.
