From Riemann to Differential Geometry and Relativity

by Lizhen Ji, Athanase Papadopoulos, Sumio Yamada

Overview

This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann’s ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann’s work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.

Product Details

ISBN-13:	9783319867656
Publisher:	Springer International Publishing
Publication date:	05/19/2018
Edition description:	Softcover reprint of the original 1st ed. 2017
Pages:	647
Product dimensions:	6.10(w) x 9.25(h) x 0.06(d)

About the Author

Lizhen Ji is a specialist in geometry and the author and editor of numerous books and articles. He currently teaches at Michigan and at several universities in China, and serves as an editor for several journals.

Athanase Papadopoulos is the author/editor of 100 papers and over 20 books on mathematics and the history of mathematics. Directeur de Recherche at the CNRS, he has also been a visiting scholar at several universities and research centers (Princeton, MPI Bonn, ESI Vienna, CUNY New York, USC Los Angeles, etc.).

Sumio Yamada has worked extensively in the US and Japan (Tohoku in Sendai, followed by Gakushuin in Tokyo). He is the author of several research articles.

Lizhen Ji, A. Papadopoulos and S. Yamada have engaged in several fruitful scientific collaborations.

Table of Contents

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.