1. Differential Geometry
The ninth mathematical framework is that of differential geometry, which applies differential calculus to geometry (in this case, Euclidean geometry); that is, it deals with the local spatial behavior of differential manifolds in , primarily of codimension 1, such as curves in 2 dimensions or surfaces in 3 dimensions. In any n dimensions, a hypersurface is a differential manifold of codimension 1.
1.1 Differential varieties
Definition (differential manifold). A differential manifold is a topological manifold—with or without a boundary—in which the local homeomorphisms in the definition of a topological manifold...
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Differential Geometry
Theory of Dimension II: “Metric” Dimensions
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