A Comprehensive Introduction to Differential Geometry, Vol. 5 - ISBN:0914098888

A Comprehensive Introduction to Differential Geometry, Vol. 5

Date: 13 April 2011, 00:42

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Somewhat to my surprise, the second volume of these notes came out more or less as I had planned. Actually, that statement is only half true, for only half the material which I had planned to write has come out at all; the rest will have to fit into Volume III, which I pray will be the last. This Volume ends at a suitable stopping point, when we have finally gotten to the fanciest definition of a connection, but hardly begun to start spouting theorems. A glance at the Table of Contents will show that the semi-historical path promised in Volume I really has been followed. The most decisive encounters with classical differential geometry occur in Chapters 3 and 4, which are divided into parts; some parts present the classical papers, and other parts explain them. It is possible to get through the notes without reading any of the classical works themselves, but the easy way out misses all the fun. The students in my class found Gauss exciting, and while they found Riemann's own words bewildering, they were amazed when they learned what Riemann had been trying to say.

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