Skip to main content
SpringerLink
Log in

The Riemann Legacy

Riemannian Ideas in Mathematics and Physics

  • Book
  • © 1997

Overview

Authors:
  1. Krzysztof Maurin

    1. Division of Mathematical Methods in Physics, University of Warsaw, Warsaw, Poland

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 417)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
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

Licence this eBook for your library

Institutional subscriptions

Table of contents (59 chapters)

  1. Front Matter

    Pages i-xxii
    Download chapter PDF

  3. General Structures of Mathematics

    1. Front Matter

      Pages 119-119
      Download chapter PDF

    2. Differentiable Structures. Tangent Spaces. Vector Fields

      • Krzysztof Maurin
      Pages 121-133

    3. Projective (Inverse) Limits of Topological Spaces

      • Krzysztof Maurin
      Pages 134-136

    4. Inductive Limits. Presheaves. Covering Defined by Presheaf

      • Krzysztof Maurin
      Pages 137-147

    5. Algebras. Groups, Tensors, Clifford, Grassmann, and Lie Algebras. Theorems of Bott-Milnor, Wedderburn, and Hurwitz

      • Krzysztof Maurin
      Pages 148-162

    6. Fields and their Extensions

      • Krzysztof Maurin
      Pages 163-174

    7. Galois Theory. Solvable Groups

      • Krzysztof Maurin
      Pages 175-183

    8. Ruler and Compass Constructions. Cyclotomic Fields. Kronecker-Weber Theorem

      • Krzysztof Maurin
      Pages 184-188

    9. Algebraic and Transcendental Elements

      • Krzysztof Maurin
      Pages 189-190

    10. Weyl principle

      • Krzysztof Maurin
      Pages 191-193

    11. Topology of Compact Lie Groups

      • Krzysztof Maurin
      Pages 194-195

    12. Representations of Compact Lie Groups

      • Krzysztof Maurin
      Pages 196-209
Back to top

Keywords

About this book

very small domain (environment) affects through analytic continuation the whole of Riemann surface, or analytic manifold . Riemann was a master at applying this principle and also the first who noticed and emphasized that a meromorphic function is determined by its 'singularities'. Therefore he is rightly regarded as the father of the huge 'theory of singularities' which is developing so quickly and whose importance (also for physics) can hardly be overe~timated. Amazing and mysterious for our cognition is the role of Euclidean space. Even today many philosophers believe (following Kant) that 'real space' is Euclidean and other spaces being 'abstract constructs of mathematicians, should not be called spaces'. The thesis is no longer tenable - the whole of physics testifies to that. Nevertheless, there is a grain of truth in the 3 'prejudice': E (three-dimensional Euclidean space) is special in a particular way pleasantly familiar to us - in it we (also we mathematicians!) feel particularly 'confident' and move with a sense of greater 'safety' than in non-Euclidean spaces. For this reason perhaps, Riemann space M stands out among the multitude of 'interesting geometries'. For it is: 1. Locally Euclidean, i. e. , M is a differentiable manifold whose tangent spaces TxM are equipped with Euclidean metric Uxi 2. Every submanifold M of Euclidean space E is equipped with Riemann natural metric (inherited from the metric of E) and it is well known how often such submanifolds are used in mechanics (e. g. , the spherical pendulum).

Authors and Affiliations

  • Division of Mathematical Methods in Physics, University of Warsaw, Warsaw, Poland

    Krzysztof Maurin

Bibliographic Information

  • Book Title: The Riemann Legacy

  • Book Subtitle: Riemannian Ideas in Mathematics and Physics

  • Authors: Krzysztof Maurin

  • Series Title: Mathematics and Its Applications

  • DOI: https://doi.org/10.1007/978-94-015-8939-0

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1997

  • Hardcover ISBN: 978-0-7923-4636-4Published: 31 July 1997

  • Softcover ISBN: 978-90-481-4876-9Published: 06 December 2010

  • eBook ISBN: 978-94-015-8939-0Published: 17 April 2013

  • Edition Number: 1

  • Number of Pages: XXII, 719

  • Number of Illustrations: 3 b/w illustrations

  • Additional Information: Originally published in Polish

  • Topics: Applications of Mathematics, Algebra, Geometry, Analysis

Publish with us

Policies and ethics

Back to top

Search

Navigation