Skip to main content
SpringerLink
Log in
Book cover

Natural Operations in Differential Geometry

  • Book
  • © 1993

Overview

Authors:
  1. Ivan Kolář

    1. Department of Algebra and Geometry, Faculty of Science, Masaryk University, Brno, Czechoslovakia

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Jan Slovák

    1. Department of Algebra and Geometry, Faculty of Science, Masaryk University, Brno, Czechoslovakia

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Peter W. Michor

    1. Institut für Mathematik, Universität Wien, Wien, Austria

    View author publications

    You can also search for this author in PubMed   Google Scholar

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 99.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 129.99
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 (12 chapters)

  1. Front Matter

    Pages i-3
    Download chapter PDF

  2. Manifolds and Lie Groups

    • Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 4-48

  3. Differential Forms

    • Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 49-75

  4. Bundles and Connections

    • Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 76-115

  5. Jets and Natural Bundles

    • Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 116-167

  6. Finite Order Theorems

    • Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 168-211

  7. Methods for Finding Natural Operators

    • Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 212-248

  8. Further Applications

    • Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 249-295

  9. Product Preserving Functors

    • Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 296-328

  10. Bundle Functors on Manifolds

    • Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 329-349

  11. Prolongation of Vector Fields and Connections

    • Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 350-375

  12. General Theory of Lie Derivatives

    • Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 376-393

  13. Gauge Natural Bundles and Operators

    • Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 394-416

  14. Back Matter

    Pages 417-434
    Download chapter PDF
Back to top

Keywords

About this book

The aim of this work is threefold: First it should be a monographical work on natural bundles and natural op­ erators in differential geometry. This is a field which every differential geometer has met several times, but which is not treated in detail in one place. Let us explain a little, what we mean by naturality. Exterior derivative commutes with the pullback of differential forms. In the background of this statement are the following general concepts. The vector bundle A kT* M is in fact the value of a functor, which associates a bundle over M to each manifold M and a vector bundle homomorphism over f to each local diffeomorphism f between manifolds of the same dimension. This is a simple example of the concept of a natural bundle. The fact that exterior derivative d transforms sections of A kT* M into sections of A k+1T* M for every manifold M can be expressed by saying that d is an operator from A kT* M into A k+1T* M.

Authors and Affiliations

  • Department of Algebra and Geometry, Faculty of Science, Masaryk University, Brno, Czechoslovakia

    Ivan Kolář, Jan Slovák

  • Institut für Mathematik, Universität Wien, Wien, Austria

    Peter W. Michor

Bibliographic Information

  • Book Title: Natural Operations in Differential Geometry

  • Authors: Ivan Kolář, Jan Slovák, Peter W. Michor

  • DOI: https://doi.org/10.1007/978-3-662-02950-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Hardcover ISBN: 978-3-540-56235-1Published: 04 February 1993

  • Softcover ISBN: 978-3-642-08149-1Published: 01 December 2010

  • eBook ISBN: 978-3-662-02950-3Published: 09 March 2013

  • Edition Number: 1

  • Number of Pages: VI, 434

  • Topics: Differential Geometry, Quantum Information Technology, Spintronics, Geometry, Quantum Physics

Publish with us

Policies and ethics

Back to top

Search

Navigation