Topics in differential geometry
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Topics in a Differential Geometry Course To learn more about a topic listed below, click the topic name to go to the corresponding MathWorld classroom page. Differential Geometry. Differential geometry is the field of mathematics that studies properties such as distance and curvature on surfaces and manifolds.
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Differential k -Form. It is closely related with differential topology and with the geometric aspects of the theory of differential equations.
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Grigori Perelman's proof of the Poincare conjecture using the techniques of Ricci flow demonstrated the power of the differential-geometric approach to questions in topology and highlighted the important role played by the analytic methods. Courses 2.
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Differential Geometry of Curves and Surfaces. A differential k -form is a tensor of rank k that is antisymmetric under exchange of any pair of indices.
Gaussian Curvature. Gaussian curvature is one type measure of the amount of "bending" a surface undergoes at a given point which is independent of the coordinate system used to describe it.