Differential geometry | Wikipedia audio article
Channel: wikipedia tts
Date: 25/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Differential_geometry


00:00:48 1 History of development
00:02:13 2 Branches
00:02:22 2.1 Riemannian geometry
00:04:17 2.2 Pseudo-Riemannian geometry
00:04:43 2.3 Finsler geometry
00:05:28 2.4 Symplectic geometry
00:07:24 2.5 Contact geometry
00:09:25 2.6 Complex and Kähler geometry
00:13:02 2.7 CR geometry
00:13:18 2.8 Differential topology
00:13:49 2.9 Lie groups
00:14:22 3 Bundles and connections
00:15:44 4 Intrinsic versus extrinsic
00:17:14 5 Applications



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SUMMARY
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Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. The theory of plane and space curves and surfaces in the three-dimensional Euclidean space formed the basis for development of differential geometry during the 18th century and the 19th century.
Since the late 19th century, differential geometry has grown into a field concerned more generally with the geometric structures on differentiable manifolds. Differential geometry is closely related to differential topology and the geometric aspects of the theory of differential equations. The differential geometry of surfaces captures many of the key ideas and techniques endemic to this field.