IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-662-02950-3_3.html
   My bibliography  Save this book chapter

Bundles and Connections

In: Natural Operations in Differential Geometry

Author

Listed:
  • Ivan Kolář

    (Masaryk University, Department of Algebra and Geometry, Faculty of Science)

  • Jan Slovák

    (Masaryk University, Department of Algebra and Geometry, Faculty of Science)

  • Peter W. Michor

    (Universität Wien, Institut für Mathematik)

Abstract

We begin our treatment of connections in the general setting of fiber bundles (without structure group). A connection on a fiber bundle is just a projection onto the vertical bundle. Curvature and the Bianchi identity is expressed with the help of the Frölicher-Nijenhuis bracket. The parallel transport for such a general connection is not defined along the whole of the curve in the base in general — if this is the case for all curves, the connection is called complete. We show that every fiber bundle admits complete connections. For complete connections we treat holonomy groups and the holonomy Lie algebra, a subalgebra of the Lie algebra of all vector fields on the standard fiber.

Suggested Citation

  • Ivan Kolář & Jan Slovák & Peter W. Michor, 1993. "Bundles and Connections," Springer Books, in: Natural Operations in Differential Geometry, chapter 0, pages 76-115, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-02950-3_3
    DOI: 10.1007/978-3-662-02950-3_3
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-662-02950-3_3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.