Ideas of differential geometry have permeated all parts of mathematics. Partial differential equations, topology, analysis, and many other branches of our subject have taken on a geometric patina. The recent solution of the Poincaré conjecture used geometry in surprising ways. This issue of the Notices showcases some recent developments in the geometry of Riemann. --Steven G. Krantz, Editor
John P. D'Angelo and Jeremy T. Tyson
(pp. 208)
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Robert Osserman
(pp. 220)
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Rahim Moosa
(pp. 230)
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