Differential Geometry
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Differential geometry is the field of mathematics that studies properties such as distance and curvature on surfaces and manifolds.
Differential geometry is a college-level concept and course.
Prerequisites
| Manifold: | A manifold is a topological space that is locally Euclidean, i.e., around every point, there is a neighborhood that is topologically the same as an open unit ball in some dimension. |
| Surface: | A surface is a two-dimensional piece of three-dimensional space. |
| Topology: | (1) As a branch of mathematics, topology is the mathematical study of object's properties that are preserved through deformations, twistings, and stretchings. (2) As a set, a topology is a set along with a collection of subsets that satisfy several defining properties. |