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  • © 2017

From Riemann to Differential Geometry and Relativity

  • Explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics

  • Contains expository and historical expositions motivated by Riemann's ideas

  • Includes contributions by mathematicians, physicists, philosophers and historians of science

  • Includes supplementary material: sn.pub/extras

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Softcover Book USD 199.99
Price excludes VAT (USA)
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  • Dispatched in 3 to 5 business days
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Hardcover Book USD 199.99
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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xxxiv
  2. Looking Backward: From Euler to Riemann

    • Athanase Papadopoulos
    Pages 1-94
  3. Mathematics and Physics

    1. Front Matter

      Pages 95-95
    2. Riemann’s Work on Minimal Surfaces

      • Sumio Yamada
      Pages 135-150
    3. Physics in Riemann’s Mathematical Papers

      • Athanase Papadopoulos
      Pages 151-207
    4. Cauchy and Puiseux: Two Precursors of Riemann

      • Athanase Papadopoulos
      Pages 209-235
    5. Riemann Surfaces: Reception by the French School

      • Athanase Papadopoulos
      Pages 237-291
  4. Some Recent Developments

    1. Front Matter

      Pages 365-365
    2. The Riemann–Roch Theorem

      • Norbert A’Campo, Vincent Alberge, Elena Frenkel
      Pages 389-411
    3. Metric Geometries in an Axiomatic Perspective

      • Victor Pambuccian, Horst Struve, Rolf Struve
      Pages 413-455
    4. Generalized Riemann Sums

      • Toshikazu Sunada
      Pages 457-479
    5. From Riemannian to Relativistic Diffusions

      • Jacques Franchi
      Pages 481-511

About this book

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.



Editors and Affiliations

  • Department of Mathematics, University of Michigan, Ann Arbor, USA

    Lizhen Ji

  • University of Strasbourg, CNRS, Institut de Recherche Mathématique Avancée, Strasbourg Cedex, France

    Athanase Papadopoulos

  • Department of Mathematics, Gakushuin University, Tokyo, Japan

    Sumio Yamada

About the editors

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.


Bibliographic Information

  • Book Title: From Riemann to Differential Geometry and Relativity

  • Editors: Lizhen Ji, Athanase Papadopoulos, Sumio Yamada

  • DOI: https://doi.org/10.1007/978-3-319-60039-0

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Hardcover ISBN: 978-3-319-60038-3Published: 10 October 2017

  • Softcover ISBN: 978-3-319-86765-6Published: 17 May 2018

  • eBook ISBN: 978-3-319-60039-0Published: 03 October 2017

  • Edition Number: 1

  • Number of Pages: XXXIV, 647

  • Number of Illustrations: 24 b/w illustrations

  • Topics: History of Mathematical Sciences, Differential Geometry

Buy it now

Buying options

Softcover Book USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access