IDEAS home Printed from https://ideas.repec.org/a/hin/jijmms/493217.html
   My bibliography  Save this article

On the Level Set of a Function with Degenerate Minimum Point

Author

Listed:
  • Yasuhiko Kamiyama

Abstract

For , let be an -dimensional smooth closed manifold and a smooth function. We set and assume that is attained by unique point such that is a nondegenerate critical point. Then the Morse lemma tells us that if is slightly bigger than , is diffeomorphic to . In this paper, we relax the condition on from being nondegenerate to being an isolated critical point and obtain the same consequence. Some application to the topology of polygon spaces is also included.

Suggested Citation

  • Yasuhiko Kamiyama, 2015. "On the Level Set of a Function with Degenerate Minimum Point," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2015, pages 1-6, July.
    • Handle: RePEc:hin:jijmms:493217
    DOI: 10.1155/2015/493217
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/IJMMS/2015/493217.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/IJMMS/2015/493217.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2015/493217?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    More about this item

    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:hin:jijmms:493217. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.