From Riemann to Differential Geometry and Relativity

Lizhen Ji is a specialist in geometry and the author and editor of numerous books and articles. He teaches at Michain and at several universities in China. He is the editor of several journals.Athanase Papadopoulos is the author/editor of 100 papers and about 20 books on mathematics and history of mathematics. Directeur de Recherche ar CNRS he was visiting scholar at several universities and research centres (Princeton, MPI Bonn, ESI Vienna, CUNY New York, USC Los Angeles, etc.). Sumio Yamada worked in the US and in Japan (Tohoku in Sendai and then Gakushuin in Tokyo). He is the author of several research articles. Lizhen Ji and A. papadopoulos, and A. Papadopoulos and S. Yamada, have several scientific collaborations.

Preface.- Introduction.- 1.Athanase Papadopoulos: Looking backward: From Euler to Riemann .- 2.Jeremey Gray: Riemann on geometry, physics, and philosophy - some remarks.- 3.Hubert Goenner: Some remarks on a contribution to electrodynamics by Bernhard Riemann.- 4.Christian Houzel: Riemann's Memoir Über das Verschwinden der Theta-Functionen.- 5.Sumio Yamada: Riemann's work on minimal surfaces.- 6. Athanase Papadopoulos: Physics in Riemann's mathematical papers.- 7.Athanase Papadopoulos: Cauchy and Puiseux: Two precursors of Riemann.- 8.Athanase Papadopoulos: Riemann surfaces: Reception by the French school.- 9.Ken'ichi Ohshika: The origin of the notion of manifold: from Riemann's Habilitationsvortrag onward.- 10.Franck Jedrzejewski: Deleuze et la géométrie riemannienne : une topologie des multiplicités.- 11.Arkady Plotnitsky: Comprehending the Connection of Things: Bernhard Riemann and the Architecture of Mathematical Concepts.- 12.Feng Luo: The Riemann mapping theorem and its discrete counterparts.- 13.Norbert A'Campo, Vincent Alberge and Elena Frenkel: The Riemann-Roch theorem.- 14.Victor Pambuccian, Horst Struve and Rolf Struve: Metric geometries in an axiomatic perspective.- 15.Toshikazu Sunada: Generalized Riemann sums.- 16.Jacques Franchi: From Riemannian to Relativistic Diffusions.- 17.Andreas Hermann and Emmanuel Humbert: On the Positive Mass Theorem for closed Riemannian manifolds.- 18.Marc Mars: On local characterization results in geometry and gravitation.- 19.Jean-Philippe Nicolas: The conformal approach to asymptotic analysis.- 20.Lizhen Ji: Bernhard Riemann and his work.