IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i4p591-d749377.html
   My bibliography  Save this article

Differential Geometry of Submanifolds in Complex Space Forms Involving δ -Invariants

Author

Listed:
  • Bang-Yen Chen

    (Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
    These authors contributed equally to this work.)

  • Adara M. Blaga

    (Department of Mathematics, West University of Timişoara, 300223 Timişoara, Romania
    These authors contributed equally to this work.)

  • Gabriel-Eduard Vîlcu

    (Research Center in Geometry, Faculty of Mathematics and Computer Science, University of Bucharest, Topology and Algebra, Str. Academiei 14, 70109 Bucharest, Romania
    Department of Mathematics and Informatics, Faculty of Applied Sciences, University Politehnica of Bucharest, Splaiul Independenţei 313, 060042 Bucharest, Romania
    Department of Cybernetics, Petroleum-Gas University of Ploieşti, Economic Informatics, Finance and Accountancy, Bd. Bucureşti 39, 100680 Ploieşti, Romania
    These authors contributed equally to this work.)

Abstract

One of the fundamental problems in the theory of submanifolds is to establish optimal relationships between intrinsic and extrinsic invariants for submanifolds. In order to establish such relations, the first author introduced in the 1990s the notion of δ -invariants for Riemannian manifolds, which are different in nature from the classical curvature invariants. The earlier results on δ -invariants and their applications have been summarized in the first author’s book published in 2011 Pseudo-Riemannian Geometry, δ-Invariants and Applications (ISBN: 978-981-4329-63-7). In this survey, we present a comprehensive account of the development of the differential geometry of submanifolds in complex space forms involving the δ -invariants done mostly after the publication of the book.

Suggested Citation

  • Bang-Yen Chen & Adara M. Blaga & Gabriel-Eduard Vîlcu, 2022. "Differential Geometry of Submanifolds in Complex Space Forms Involving δ -Invariants," Mathematics, MDPI, vol. 10(4), pages 1-38, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:4:p:591-:d:749377
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/4/591/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/4/591/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bang-Yen Chen & Adara M. Blaga, 2021. "Geometric Inequalities for Warped Products in Riemannian Manifolds," Mathematics, MDPI, vol. 9(9), pages 1-31, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bang-Yen Chen & Gabriel-Eduard Vîlcu, 2023. "Recent Developments on the First Chen Inequality in Differential Geometry," Mathematics, MDPI, vol. 11(19), pages 1-50, October.
    2. Vladimir Rovenski, 2022. "Geometric Inequalities for a Submanifold Equipped with Distributions," Mathematics, MDPI, vol. 10(24), pages 1-11, December.
    3. Simona Decu, 2022. "Casorati Inequalities for Spacelike Submanifolds in Sasaki-like Statistical Manifolds with Semi-Symmetric Metric Connection," Mathematics, MDPI, vol. 10(19), pages 1-15, September.

    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. Vladimir Rovenski, 2022. "Geometric Inequalities for a Submanifold Equipped with Distributions," Mathematics, MDPI, vol. 10(24), pages 1-11, December.

    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:10:y:2022:i:4:p:591-:d:749377. 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.