differentiable manifold
A "differentiable manifold" is a fundamental concept in differential geometry, enabling the use of calculus in more complex spaces than Euclidean spaces.
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Definition
C2Differential Geometry
(technical, academic)A space that locally resembles Euclidean space and supports calculus operations due to its smooth structure.
Example
- In differential geometry, a differentiable manifold allows us to extend the methods of calculus to more complex shapes.
- Tangent spaces can be defined at every point on a differentiable manifold.