Say f(z) = z^m. f' = m*z^(m-1). f'' = m*(m-1)*z^(m-2). f''/f' = (m-1)*z^(m-2-m+1) = (m-1)*z^(-1). Call K the complex curvature of f(z). -i*Conj[K] = (m-1)/(z*Length[z]). Ok. So that pile of crap right there is an intrinsic property of the mapping f: z -> z^m. It tells us that even if we were to apply the mapping to a straight line, with zero curvature, the image curve would have non-zero curvature. For m=1, a linear mapping, it produces zero, as expected.

## Wednesday, June 05, 2002

## About Me

**Name:**a. geon**Location:**United States

You know what I love most about the net? It's that on the world wide Intarweb, nobody knows you're a dog.

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## Linkage

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## Reading List

*Visual Complex Analysis*, by Tristan Needham -- an absolutely **fantastic** book, highest possible recommendation to *anyone* with calculus who likes pictures. Reads better than a novel.

The Way of Analysis, by Strichartz -- Heavy going at times, but recommended - real analysis is damn useful, and this book does a good job of presenting it.

Comprehensive Intro. to Differential Geometry, by Spivak -- beautiful, enlightening, highly recommended, but be warned, it is very challenging particularly for people like me who haven't had much prior exposure to highly rigorous texts.

Gauge Fields, Knots, and Gravity, by Baez and Munian -- another **stunning**, engrossing, entertaining book. It goes on a wild adventure ride, starting from Maxwell's Equations, to some differential geometry, to 'gauge fields' and the Yang-Mills equations, to knots, and then to general relativity. Simply outstanding.

Geometrical Methods of Mathematical Physics, by Schutz - just got this, to help me deal with Spivak's text. Looks good so far, but haven't read nearly enough to give a recommendation.

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