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Differential Geometry Paperback – Apr 14 2006

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1 of 1 people found the following review helpful
Archaic and of little historical or mathematical interest Oct. 14 2013
By Alan U. Kennington - Published on Amazon.com
Format: Paperback Verified Purchase
Regrettably, I have to report that this book "Differential Geometry" by William Caspar Graustein is of little interest to the modern reader. I had hoped that it would throw some light on the state of differential geometry in the 1930s, but the modernity of this book is somewhere between Gauss and Darboux. Nevertheless, I'm grateful to Dover for keeping it in print. It's good to keep the old books alive.

Graustein only very peripherally acknowledges the work of Riemann, Christoffel, Levi-Civita and Weyl in two pages, almost at the end of the book. He gives a very brief mention of Weyl's idea of an affine connection, which generalizes the Riemannian metric.

You will find almost no modern differential geometry in this book. Even the idea of a "tangent vector" is introduced only as a unit vector tangent to a curve. There are no tensors, no affine connection or Riemannian metric (apart from a very brief allusion), no topology, no differential forms, etc. etc. It's just the geometry of surfaces embedded in Euclidean 3-space, in the 19th century idiom of Gauss and Darboux. However, I do not regret buying it. It's good to have a book which gives me the Gaussian differential geometry in a well-presented compact format.
book is 75 years old (out of date). some if the calculus notation was not reconizable. graphics was poor. Jan. 7 2014
By Brian Coughlin - Published on Amazon.com
Format: Hardcover
book is 75 years old (out of date). some if the calculus notation was not recognizable. graphics was poor or non existent.