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A New Algebraic Inequality and Some Applications in Submanifold Theory

Author

Listed:
  • Ion Mihai

    (Department of Mathematics, University of Bucharest, 010014 Bucharest, Romania
    These authors contributed equally to this work.)

  • Radu-Ioan Mihai

    (Faculty of Mathematics and Computer Science, University of Bucharest, 010014 Bucharest, Romania
    These authors contributed equally to this work.)

Abstract

We give a simple proof of the Chen inequality involving the Chen invariant δ ( k ) of submanifolds in Riemannian space forms. We derive Chen’s first inequality and the Chen–Ricci inequality. Additionally, we establish a corresponding inequality for statistical submanifolds.

Suggested Citation

  • Ion Mihai & Radu-Ioan Mihai, 2021. "A New Algebraic Inequality and Some Applications in Submanifold Theory," Mathematics, MDPI, vol. 9(11), pages 1-10, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1175-:d:560373
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    References listed on IDEAS

    as
    1. Paul Vos, 1989. "Fundamental equations for statistical submanifolds with applications to the Bartlett correction," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(3), pages 429-450, September.
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