IDEAS home Printed from https://ideas.repec.org/a/hin/jnlamp/7590847.html
   My bibliography  Save this article

Burgers’ Equations in the Riemannian Geometry Associated with First-Order Differential Equations

Author

Listed:
  • Z. Ok Bayrakdar
  • T. Bayrakdar

Abstract

We construct metric connection associated with a first-order differential equation by means of the generator set of a Pfaffian system on a submanifold of an appropriate first-order jet bundle. We firstly show that the inviscid and viscous Burgers’ equations describe surfaces attached to an ODE of the form with certain Gaussian curvatures. In the case of PDEs, we show that the scalar curvature of a three-dimensional manifold encoding a system of first-order PDEs is determined in terms of the integrability condition and the Gaussian curvatures of the surfaces corresponding to the integral curves of the vector fields which are annihilated by the contact form. We see that an integral manifold of any PDE defines intrinsically flat and totally geodesic submanifold.

Suggested Citation

  • Z. Ok Bayrakdar & T. Bayrakdar, 2018. "Burgers’ Equations in the Riemannian Geometry Associated with First-Order Differential Equations," Advances in Mathematical Physics, Hindawi, vol. 2018, pages 1-8, February.
    • Handle: RePEc:hin:jnlamp:7590847
    DOI: 10.1155/2018/7590847
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/AMP/2018/7590847.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/AMP/2018/7590847.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2018/7590847?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:jnlamp:7590847. 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.