Manifolds and Differential Geometry (Graduate Studies in

Format: Hardcover

Language: English

Format: PDF / Kindle / ePub

Size: 10.63 MB

The apparatus of differential geometry is that of calculus on manifolds: this includes the study of manifolds, tangent bundles, cotangent bundles, differential forms, exterior derivatives, integrals of p-forms over p-dimensional submanifolds and Stokes' theorem, wedge products, and Lie derivatives. To illustrate this idea, consider the ancient belief that the Earth was flat as contrasted with the modern evidence that it is round. Immanuel Kant argued that there is only one, absolute, geometry, which is known to be true a priori by an inner faculty of mind: Euclidean geometry was synthetic a priori. [2] This dominant view was overturned by the revolutionary discovery of non-Euclidean geometry in the works of Gauss (who never published his theory), Bolyai, and Lobachevsky, who demonstrated that ordinary Euclidean space is only one possibility for development of geometry.

Pages: 671

Publisher: American Mathematical Society (November 25, 2009)

ISBN: 0821848151

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