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Differential geometry is a branch of mathematics that applies differential and integral calculus to planes, space curves, surfaces in three-dimensional space, and geometric structures on differentiable manifolds. It is closely related to differential topology and to the geometric aspects of the theory of differential equations.

A broad range of topics may be studied in differential geometry, and those include, but are not limited to:

- Curves in the plane
- Famous plane curves
- Alternative ways of plotting curves
- New curves from old
- Determining a plane curve from its curvature
- Global properties of plane curves
- Curves in space
- Construction of space curves
- Calculus on Euclidean space
- Surfaces in Euclidean space
- Nonorientable surfaces
- Metrics on surfaces
- Shape and curvature
- Ruled surfaces
- Surfaces of revolution and constant curvature
- A selection of minimal surfaces
- Intrinsic surface geometry
- Asymptotic curves and geodesics on surfaces
- Principal curves and umbilic points
- Canal surfaces and cyclides of Dupin
- The theory of surfaces of constant negative curvature
- Minimal surfaces via complex variables
- Rotation and animation using quaternions
- Differentiable manifolds
- Riemannian manifolds
- Abstract surfaces and their geodesics
- The Gauss-Bonnet theorem

There are many places to find great books on differential geometry, and as usual, a good place to start looking is Amazon.com. Remember to check out the Journal of Differential Geometry which is published under the copyright of Lehigh University in Bethlehem, Pennsylvania.

Other useful links may include:

- Differential Geometry and General Relativity Lecture Notes from Hofstra University
- Differential Geometry Lecture Notes from the Budapest Semesters in Mathematics
- Differential Geometry Tutorial

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- Provide specific insight for homework assignments.
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