184985

Springer, Dordrecht

2017

647 Pages

ISBN 978-3-319-60038-3

From Riemann to differential geometry and relativity

Edited by

Lizhen Ji , Athanase Papadopoulos , Sumio Yamada

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.

Publication details

Full citation:

Ji, L. , Papadopoulos, A. , Yamada, S. (eds) (2017). From Riemann to differential geometry and relativity, Springer, Dordrecht.

Table of Contents

Looking backward

Papadopoulos Athanase

1-94

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Riemann's work on minimal surfaces

Yamada Sumio

135-150

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Physics in Riemann's mathematical papers

Papadopoulos Athanase

151-207

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Cauchy and Puiseux

Papadopoulos Athanase

209-235

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Riemann surfaces

Papadopoulos Athanase

237-291

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The origin of the notion of manifold

Ohshika Ken'ichi

295-309

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Deleuze et la géométrie Riemannienne

Jedrzejewski Franck

311-328

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Comprehending the connection of things

Plotnitsky Arkady

329-363

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The Riemann–Roch theorem

A'Campo Norbert; Alberge Vincent; Frenkel Elena

389-411

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Metric geometries in an axiomatic perspective

Pambuccian Victor; Struve Horst; Struve Rolf

413-455

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Generalized Riemann sums

Sunada Toshikazu

457-479

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On the positive mass theorem for closed Riemannian manifolds

Hermann Andreas; Humbert Emmanuel

515-540

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The conformal approach to asymptotic analysis

Nicolas Jean-Philippe

571-609

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Bernhard Riemann and his work

Ji Lizhen

613-635

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