Sep 28

Curvature and Betti Numbers. (AM-32) (Annals of Mathematics

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Language: English

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Thurston's Three-Dimensional Geometry and Topology, Volume 1 (Princeton University Press, 1997) is a considerable expansion of the first few chapters of these notes. With the help of general coordinate transformations, the Christoffel symbols are defined in the Riemannian space. In particular, this means that distances measured along the surface (intrinsic) are unchanged. Curvature K(x) as the expectation E[j(f,x)] over a probability space of scalar functions f is therefore zero too. [Feb 20, 2012:] Index expectation ( ArXiv brings in some probability theory.

Pages: 190

Publisher: Princeton University Press (January 20, 1954)

ISBN: 0691095833

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