From Riemann to Differential Geometry and Relativity / edited by Lizhen Ji, Athanase Papadopoulos, Sumio Yamada.

Format:

Book

Contributor:

Ji, Lizhen., Editor.

Papadopoulos, Athanase, Editor.

Yamada, Sumio, Editor.

Language:

English

Subjects (All):

Mathematics.

History.

Geometry, Differential.

History of Mathematical Sciences.

Differential Geometry.

Local Subjects:

History of Mathematical Sciences.

Differential Geometry.

Physical Description:

1 online resource (XXXIV, 647 p. 24 illus.)

Edition:

1st ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

Summary:

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.

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.

Notes:

Includes bibliographical references at the end of each chapters and index.

ISBN:

3-319-60039-7