Klientų aptarnavimas: +370 652 87781

Pagalba | Naujas vartotojas | Prisijungti

El. knyga: From Riemann to Differential Geometry and Relativity

Edited by Lizhen Ji, Edited by Sumio Yamada, Edited by Athanase Papadopoulos

Formatas: EPUB+DRM
Išleidimo metai: 03-Oct-2017
Leidėjas: Springer International Publishing AG
Kalba: eng
ISBN-13: 9783319600390

Kitos knygos pagal šią temą:

Formatas - EPUB+DRM
Kaina: 197,59 €*
* ši kaina yra galutinė, t.y. papildomos nuolaidos nebus taikomos
Įdėti į krepšelį
Įtraukti į pageidavimų sąrašą
Ši e-knyga skirta tik asmeniniam naudojimui. El. knygos nėra grąžinamos.

Formatas: EPUB+DRM
Išleidimo metai: 03-Oct-2017
Leidėjas: Springer International Publishing AG
Kalba: eng
ISBN-13: 9783319600390

Kitos knygos pagal šią temą:

DRM apribojimai

Kopijuoti:

neleidžiama
Spausdinti:

neleidžiama
El. knygos naudojimas:

Skaitmeninių teisių valdymas (DRM)
Leidykla pateikė šią knygą šifruota forma, o tai reiškia, kad norint ją atrakinti ir perskaityti reikia įdiegti nemokamą programinę įrangą. Norint skaityti šią el. knygą, turite susikurti Adobe ID . Daugiau informacijos čia. El. knygą galima atsisiųsti į 6 įrenginius (vienas vartotojas su tuo pačiu Adobe ID).

Reikalinga programinė įranga
Norint skaityti šią el. knygą mobiliajame įrenginyje (telefone ar planšetiniame kompiuteryje), turite įdiegti šią nemokamą programėlę: PocketBook Reader (iOS / Android)

Norint skaityti šią el. knygą asmeniniame arba „Mac“ kompiuteryje, Jums reikalinga Adobe Digital Editions “ (tai nemokama programa, specialiai sukurta el. knygoms. Tai nėra tas pats, kas „Adobe Reader“, kurią tikriausiai jau turite savo kompiuteryje.)

Negalite skaityti šios el. knygos naudodami „Amazon Kindle“.

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.

Preamble

1 Looking Backward: From Euler to Riemann

(96)

Amanase Papadopoulos

1 Introduction

(8)

2 Functions

(10)

3 Elliptic Integrals

(10)

4 Abelian Functions

(2)

5 Hypergeometric Series

(1)

6 The Zeta Function

(7)

7 On Space

(6)

8 Topology

(14)

9 Differential Geometry

(6)

10 Trigonometric Series

(10)

11 Integration

(2)

12 Conclusion

(19)

References

(16)

Part I Mathematics and Physics

2 Riemann on Geometry, Physics, and Philosophy---Some Remarks

(14)

Jeremy Gray

1 Introduction

(1)

2 The Hypotheses

(3)

3 Influences

101

(5)

4 Heat Diffusion and the Commentatio

106

(5)

References

108

(3)

3 Some Remarks on "A Contribution to Electrodynamics" by Bernhard Riemann

111

(14)

Hubert Goenner

1 Introduction Ill

2 Riemann's New Result of 1858: The Retarded Potential

112

(2)

3 Gauss, Weber, and Riemann on Electrodynamic Interaction

114

(3)

4 Riemann's Paper

117

(2)

5 Concluding Remarks

119

(6)

References

122

(3)

4 Riemann's Memoir Uber das Verschwinden der υ-Functionen

125

(10)

Christian Houzel

1 Jacobi's Inversion Problem

125

(3)

2 A Crucial Observation on Theta Functions

128

(1)

3 The First Step of Riemann's Proof

129

(1)

4 The Second Step of Riemann's Proof

130

(1)

5 The Conclusion of the Proof

130

(3)

6 Later Developments

133

(2)

References

133

(2)

5 Riemann's Work on Minimal Surfaces

135

(16)

Sumio Yamada

1 Introduction

135

(1)

2 On the Surface of Least Area with a Given Boundary

136

(11)

3 Representation Formulas by Riemann and Weierstrass-Enneper

147

(2)

4 Closing Remarks

149

(2)

References

150

(1)

6 Physics in Riemann's Mathematical Papers

151

(58)

Athanase Papadopoulos

1 Introduction

151

(11)

2 Function Theory and Riemann Surfaces

162

(11)

3 Riemann's Memoir on Trigonometric Series

173

(8)

4 Riemann's Habilitationsvortrag 1854---Space and Matter

181

(12)

5 The Commentatio and the Gleichgewicht der Electricitat

193

(2)

6 Riemann's Other Papers

195

(4)

7 Conclusion

199

(10)

References

199

(10)

7 Cauchy and Puiseux: Two Precursors of Riemann

209

(28)

Athanase Papadopoulos

1 Introduction

209

(1)

2 Algebraic Functions and Uniformization

210

(2)

3 Puiseux and Uniformization

212

(8)

4 Cauchy and His Work on Functions of a Complex Variable

220

(10)

5 Uniformization Again

230

(7)

References

232

(5)

8 Riemann Surfaces: Reception by the French School

237

(58)

Athanase Papadopoulos

1 Introduction

238

(2)

2 Riemann Surfaces

240

(4)

3 The Nineteenth-Century French Treatises on Analysis

244

(27)

4 Simart's Dissertation

271

(4)

5 Other French Dissertations and Other Works of Riemann

275

(6)

6 On the Relations Between the French and German Mathematicians

281

(3)

7 In a Way of Conclusion

284

(11)

References

286

(9)

Part II Philosophy

9 The Origin of the Notion of Manifold: From Riemann's Habilitationsvortrag Onward

295

(16)

Ken'ichi Ohshika

1 Introduction

295

(1)

2 Kantian Worldview

296

(2)

3 Riemann's Habilitationsvortrag

298

(3)

4 Poincare's Analysis Situs

301

(4)

5 Definitions Using Local Charts According to Hilbert, Weyl, Kneser and Veblen-Whitehead

305

(3)

6 Conclusion: Philosophical Significance

308

(3)

References

308

(3)

10 Deleuze et la Geometrie Riemannienne: Une Topologie des Multiplicites

311

(18)

Franck Jedrzejewski

1 Introduction

311

(1)

2 Variete et multiplicite

312

(4)

3 Espaces, mesures et multiplicites

316

(3)

4 Typologies des multiplicites

319

(5)

5 Conclusion

324

(1)

6 Extended English Abstract

325

(4)

References

327

(2)

11 Comprehending the Connection of Things: Bernhard Riemann and the Architecture of Mathematical Concepts

329

(38)

Arkady Plotnitsky

1 Introduction

329

(7)

2 Philosophy: Planes of Thought and the Architecture of Concepts

336

(7)

3 Mathematics: Space, Geometry, and the Concept of Manifold

343

(10)

4 Physics: "The Reality Underlying Space"

353

(8)

5 Conclusion

361

(6)

References

362

(5)

Part III Some Recent Developments

12 The Riemann Mapping Theorem and Its Discrete Counterparts

367

(22)

Feng Luo

1 Introduction

367

(1)

2 Koebe-Andreev-Thurston's Circle Packing Theorem

368

(7)

3 A Discrete Uniformization Theorem

375

(14)

References

387

(2)

13 The Riemann-Roch Theorem

389

(24)

Norbert A'Campo

Vincent Alberge

Elena Frenkel

1 Introduction

389

(2)

2 Line Bundles

391

(5)

3 Sheaf Cohomology

396

(4)

4 Further Preparations

400

(5)

5 The Riemann-Roch Theorem

405

(2)

6 Divisors and the Riemann-Roch Theorem

407

(2)

7 The Use of the Riemann-Roch Theorem in Teichmuller's Work

409

(4)

References

410

(3)

14 Metric Geometries in an Axiomatic Perspective

413

(44)

Victor Pambuccian

Horst Struve

Rolf Struve

1 Introduction

414

(8)

2 Metric Planes

422

(11)

3 Higher-Dimensional Metric Spaces

433

(3)

4 The Dimension-Free Case

436

(1)

5 Projective-Metric Geometry

437

(5)

6 Cayley-Klein Geometries

442

(15)

References

451

(6)

15 Generalized Riemann Sums

457

(24)

Toshikazu Sunada

1 Introduction

457

(3)

2 Generalized Riemann Sums

460

(2)

3 Classical Example 1

462

(2)

4 Classical Example 2

464

(4)

5 The Inclusion-Exclusion Principle

468

(4)

6 Generalized Poisson Summation Formulas

472

(3)

7 Is Zdprim a Quasicrystal?

475

(6)

References

478

(3)

16 From Riemannian to Relativistic Diffusions

481

(34)

Jacques Franchi

1 Introduction

481

(3)

2 Euclidean Brownian Motion

484

(2)

3 Riemannian Brownian Motion

486

(1)

4 The Relativistic Dudley Diffusion in Minkowski Space

487

(3)

5 The Lorentzian Frame Bundle G(M) over (M, g)

490

(3)

6 The Basic Relativistic Diffusion

493

(7)

7 Covariant Ξ-relativistic Diffusions

500

(3)

8 Example of Robertson-Walker (R-W) Manifolds

503

(6)

9 Sectional Relativistic Diffusion

509

(6)

References

510

(5)

Part IV Relativity

17 On the Positive Mass Theorem for Closed Riemannian Manifolds

515

(26)

Andreas Hermann

Emmanuel Humbert

1 Introduction

515

(2)

2 ADM Mass in General Relativity

517

(10)

3 The Mass of a Closed Manifold

527

(5)

4 Equivalence of the Two Positive Mass Conjectures

532

(1)

5 Some Recent Results on the Positive Mass Conjecture

533

(2)

6 An Idea of the Proof of Theorem 5.2

535

(3)

7 Preservation of Mass by Surgery

538

(3)

References

539

(2)

18 On Local Characterization Results in Geometry and Gravitation

541

(30)

Marc Mars

1 Introduction

541

(1)

2 Classical Characterizations

542

(4)

3 Local Characterizations of the Schwarzschild and Kruskal Spacetimes

546

(9)

4 Local Characterization of pp-Waves and Related Spacetimes

555

(4)

5 Local Characterizations of the Kerr, Kerr-Newman and Kerr-De Sitter Metrics

559

(12)

References

567

(4)

19 The Conformal Approach to Asymptotic Analysis

571

(42)

Jean-Philippe Nicolas

1 Introduction

571

(3)

2 Conformal Compactification

574

(7)

3 Peeling

581

(12)

4 Conformal Scattering

593

(14)

5 Concluding Remarks

607

(6)

References

607

(6)

Part V Concluding
Chapter

20 Bernhard Riemann and His Work

613

(24)

Lizhen Ji

1 Introduction

613

(2)

2 Riemann's Work I: His Best Known Works

615

(4)

3 Riemann's Work II: Some Little Known or Even Unknown Works

619

(2)

4 Riemann's Publications and his Impact

621

(8)

5 How Riemann Developed

629

(3)

6 People Who Influenced Riemann

632

(5)

References

634

(3)

Index

637

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.

Daugiau apie elektronines knygas

Pastovi nuoroda: https://www.kriso.lt/db/97833196003906e.html

Raktažodžiai:

El. knyga: From Riemann to Differential Geometry and Relativity

DRM apribojimai

Kopijuoti:

Spausdinti:

El. knygos naudojimas:

Paskyra ir nustatymai

Paieška

Ieškoti duomenų bazėje

Patikslinti paiešką

Temos E-knygų temos

Pasirinkti pirkinių krepšelį