From Riemann to Differential Geometry and Relativity

• Corporate Author: SpringerLink (Online service)
• Other Authors: Ji, Lizhen (Editor), Papadopoulos, Athanase (Editor), Yamada, Sumio (Editor)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Subjects: Mathematics.; Differential geometry.; History.; History of Mathematical Sciences.; Differential Geometry.

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 c...

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.