Riemann, Bernhard

We now wish to introduce a still deeper form of geometry as first suggested by Bernhard Riemann (Sidebar 13.2). Riemann s formalism makes possible a distinction between the space of vectors whose metrical relationships are specified by the metric M and an associated linear manifold by which the vectors and metric are parametrized. Let be an element of a linear manifold (in general, having no metric character) that can uniquely identify the state of a collection of metrical objects X). The Riemannian geometry permits the associated metric M to itself be a function of the state,... 

Georg Friedrich Bernhard Riemann was the second of six children bom into the family of an impoverished Lutheran minister in lower Saxony, near modem Hannover, Germany. Riemann suffered from childhood malnutrition and was prone to excessive timidity, sickness, and nervous breakdowns throughout his difficult life, which ended in Italy while he was attempting recuperation from chronic tuberculosis (with a wife and young child at his side) at age 39. 

For excellent insight into Riemann and his mathematics (primarily focusing on the Riemann zeta function and the Riemann hypothesis ), see J. Derbyshire. Prime Obsession Bernhard Riemann and the Greatest Unsolved Problem in Mathematics (Penguin, New York, 2004).]... 

Reichhn Robin L., 948 Reimers Jeffrey R., 362 Reines Frederick, 593 Reinhoudt David N., 978 Rejewski Marian, 1003 Ridard Jacqueline, 469 Riemann Georg Friedrich Bernhard, 560 RipoU Daniel R., 819 Ritz Walther, 232, 239 Robb Michael A., 313, 334 Roch Jean-Fran9ois, 47 Rodnikova Margarita, 89, 867... 

Riemann George Friedrich Bernhard (1826-1866) Ger. math., introduced idea of finite but unbounded space (Riemann s functions and prime numbers), devised innovative geometry of the saddle-like space, theory of electromagnetic action Riga Alan T. (1937-) US chem.., polymers and pharmacy science, lubricants and biosensors (book Material characterization by TA 1991)... 

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