Natural Operations in Differential Geometry

  • Ivan Kolář
  • Jan Slovák
  • Peter W. Michor

Table of contents

  1. Front Matter
    Pages i-3
  2. Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 4-48
  3. Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 49-75
  4. Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 76-115
  5. Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 116-167
  6. Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 168-211
  7. Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 212-248
  8. Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 249-295
  9. Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 296-328
  10. Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 329-349
  11. Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 350-375
  12. Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 376-393
  13. Ivan Kolář, Jan Slovák, Peter W. Michor
    Pages 394-416
  14. Back Matter
    Pages 417-434

About this book

Introduction

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.

Keywords

Category over Manifolds Jet Natural Bundle Natural Operator differential geometry manifold mathematical physics

Authors and affiliations

  • Ivan Kolář
    • 1
  • Jan Slovák
    • 1
  • Peter W. Michor
    • 2
  1. 1.Department of Algebra and Geometry, Faculty of ScienceMasaryk UniversityBrnoCzechoslovakia
  2. 2.Institut für MathematikUniversität WienWienAustria

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-02950-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-08149-1
  • Online ISBN 978-3-662-02950-3
  • About this book