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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
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    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.
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    Cited by:

    1. Vladimir Rovenski, 2022. "Geometric Inequalities for a Submanifold Equipped with Distributions," Mathematics, MDPI, vol. 10(24), pages 1-11, December.
    2. 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.
    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.

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

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