IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i5p537-d510209.html
   My bibliography  Save this article

Riccati PDEs That Imply Curvature-Flatness

Author

Listed:
  • Iulia Hirica

    (Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, Sector 1, RO-010014 Bucharest, Romania
    These authors contributed equally to this work.)

  • Constantin Udriste

    (Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, RO-060042 Bucharest, Romania
    These authors contributed equally to this work.
    Second address: Academy of Romanian Scientists, Ilfov 3, Sector 5, RO-050044 Bucharest, Romania.)

  • Gabriel Pripoae

    (Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, Sector 1, RO-010014 Bucharest, Romania
    These authors contributed equally to this work.)

  • Ionel Tevy

    (Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independentei 313, Sector 6, RO-060042 Bucharest, Romania
    These authors contributed equally to this work.)

Abstract

In this paper the following three goals are addressed. The first goal is to study some strong partial differential equations (PDEs) that imply curvature-flatness, in the cases of both symmetric and non-symmetric connection. Although the curvature-flatness idea is classic for symmetric connection, our main theorems about flatness solutions are completely new, leaving for a while the point of view of differential geometry and entering that of PDEs. The second goal is to introduce and study some strong partial differential relations associated to curvature-flatness. The third goal is to introduce and analyze some vector spaces of exotic objects that change the meaning of a generalized Kronecker delta projection operator, in order to discover new PDEs implying curvature-flatness. Significant examples clarify some ideas.

Suggested Citation

  • Iulia Hirica & Constantin Udriste & Gabriel Pripoae & Ionel Tevy, 2021. "Riccati PDEs That Imply Curvature-Flatness," Mathematics, MDPI, vol. 9(5), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:537-:d:510209
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/5/537/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/5/537/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Constantin Udriste & Ionel Tevy, 2020. "Geometric Dynamics on Riemannian Manifolds," Mathematics, MDPI, vol. 8(1), pages 1-14, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Iulia Hirica & Constantin Udriste & Gabriel Pripoae & Ionel Tevy, 2020. "Least Squares Approximation of Flatness on Riemannian Manifolds," Mathematics, MDPI, vol. 8(10), pages 1-18, October.

    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:gam:jmathe:v:9:y:2021:i:5:p:537-:d:510209. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.