IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4614-7867-6_10.html
   My bibliography  Save this book chapter

The Tensor Description of Embedded Surfaces

In: Introduction to Tensor Analysis and the Calculus of Moving Surfaces

Author

Listed:
  • Pavel Grinfeld

    (Drexel University, Department of Mathematics)

Abstract

We have finally arrived at the subject of surfaces. This topic is extraordinarily rich and it lets tensor calculus shine at its brightest. We will focus on two-dimensional surfaces in three-dimensional Euclidean spaces. The Euclidean space in which the surface is embedded is called the ambient space. The analysis presented in this chapter is easily extended to hypersurfaces of any dimension. A hypersurface is a differentiable (n − 1)-dimensional subspace of an n-dimensional space. That is, a hypersurface is characterized by a codimension of 1, codimension being the difference between the dimensions of the ambient and embedded spaces. Curves, the subject of Chap. 13, embedded in the three-dimensional Euclidean space have codimension two.

Suggested Citation

  • Pavel Grinfeld, 2013. "The Tensor Description of Embedded Surfaces," Springer Books, in: Introduction to Tensor Analysis and the Calculus of Moving Surfaces, edition 127, chapter 0, pages 161-184, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-7867-6_10
    DOI: 10.1007/978-1-4614-7867-6_10
    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:978-1-4614-7867-6_10. 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.