differential geometry: Development of Differential Geometry

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Encyclopedia—differential geometry

Development of Differential Geometry

Differential geometry was founded by Gaspard Monge and C. F. Gauss in the beginning of the 19th cent. Important contributions were made by many mathematicians during the 19th cent., including B. Riemann, E. B. Christoffel, and C. G. Ricci. This work was collected and systematized at the end of the century by J. G. Darboux and Luigi Bianchi. The importance of differential geometry may be seen from the fact that Einstein's general theory of relativity is formulated entirely in terms of the differential geometry, in tensor notation, of a four-dimensional manifold combining space and time.

Sections in this article:

Introduction
The Analysis of Curves
The Analysis of Surfaces
Development of Differential Geometry

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