From Riemann to differential geometry and relativity

✍ Scribed by Ji, Lizhen; Papadopoulos, Athanase; Yamada, Sumio (eds.)

• Publisher: Springer
• Year: 2017
• Tongue: English
• Leaves: 664
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xxxiv
Looking Backward: From Euler to Riemann (Athanase Papadopoulos)....Pages 1-94
Front Matter ....Pages 95-95
Riemann on Geometry, Physics, and Philosophy—Some Remarks (Jeremy Gray)....Pages 97-110
Some Remarks on “A Contribution to Electrodynamics” by Bernhard Riemann (Hubert Goenner)....Pages 111-123
Riemann’s Memoir Über das Verschwinden der (\vartheta )-Functionen (Christian Houzel)....Pages 125-134
Riemann’s Work on Minimal Surfaces (Sumio Yamada)....Pages 135-150
Physics in Riemann’s Mathematical Papers (Athanase Papadopoulos)....Pages 151-207
Cauchy and Puiseux: Two Precursors of Riemann (Athanase Papadopoulos)....Pages 209-235
Riemann Surfaces: Reception by the French School (Athanase Papadopoulos)....Pages 237-291
Front Matter ....Pages 293-293
The Origin of the Notion of Manifold: From Riemann’s Habilitationsvortrag Onward (Ken’ichi Ohshika)....Pages 295-309
Deleuze et la Géométrie Riemannienne: Une Topologie des Multiplicités (Franck Jedrzejewski)....Pages 311-328
Comprehending the Connection of Things: Bernhard Riemann and the Architecture of Mathematical Concepts (Arkady Plotnitsky)....Pages 329-363
Front Matter ....Pages 365-365
The Riemann Mapping Theorem and Its Discrete Counterparts (Feng Luo)....Pages 367-388
The Riemann–Roch Theorem (Norbert A’Campo, Vincent Alberge, Elena Frenkel)....Pages 389-411
Metric Geometries in an Axiomatic Perspective (Victor Pambuccian, Horst Struve, Rolf Struve)....Pages 413-455
Generalized Riemann Sums (Toshikazu Sunada)....Pages 457-479
From Riemannian to Relativistic Diffusions (Jacques Franchi)....Pages 481-511
Front Matter ....Pages 513-513
On the Positive Mass Theorem for Closed Riemannian Manifolds (Andreas Hermann, Emmanuel Humbert)....Pages 515-540
On Local Characterization Results in Geometry and Gravitation (Marc Mars)....Pages 541-570
The Conformal Approach to Asymptotic Analysis (Jean-Philippe Nicolas)....Pages 571-609
Front Matter ....Pages 611-611
Bernhard Riemann and His Work (Lizhen Ji)....Pages 613-635
Back Matter ....Pages 637-647

✦ Subjects

Geometry, Differential;Relativity (Physics);MATHEMATICS / Geometry / General